fix(nir): update tables with correct data

1 files changed, 176 insertions, 202 deletions

diff --git a/nir/nir.tex b/nir/nir.tex
index 2a5a009..cd3e5bb 100644
--- a/nir/nir.tex
+++ b/nir/nir.tex
@@ -5,7 +5,7 @@
 \course{5}

 \group{531}

 \author{Гущина Андрея Юрьевича}

-\satitle{д.ф.-м.н., доцент}

+\satitle{д.ф.-м.н., профессор}

 \saname{М. Б. Абросимов}

 \date{2024}

 

@@ -349,8 +349,8 @@ $fg(G)$. В первой колонке указаны возможные зна
   \begin{tabular}{|c|c|c|c|c|c|c|}

   \hline

     $i(G)$ \textbackslash{} $fg(G)$ & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline

-    1 & 8 & 1 & 1 & 0 & 0 & 0  \\ \hline

-    2 & 16 & 1 & 0 & 0 & 0 & 0  \\ \hline

+    1 & 9 & 1 & 1 & 0 & 0 & 0  \\ \hline

+    2 & 15 & 1 & 0 & 0 & 0 & 0  \\ \hline

     3 & 5 & 0 & 0 & 0 & 0 & 0  \\ \hline

     4 & 1 & 0 & 0 & 0 & 0 & 0  \\ \hline

     5 & 1 & 0 & 0 & 0 & 0 & 0  \\ \hline

@@ -364,10 +364,10 @@ $fg(G)$. В первой колонке указаны возможные зна
   \begin{tabular}{|c|c|c|c|c|c|c|c|}

   \hline

     $i(G)$ \textbackslash{} $fg(G)$ & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline

-    1 & 25 & 5 & 3 & 0 & 0 & 0 & 0  \\ \hline

-    2 & 66 & 11 & 7 & 2 & 0 & 0 & 0  \\ \hline

-    3 & 25 & 2 & 2 & 1 & 0 & 0 & 0  \\ \hline

-    4 & 5 & 0 & 0 & 0 & 0 & 0 & 0  \\ \hline

+    1 & 26 & 5 & 3 & 0 & 0 & 0 & 0  \\ \hline

+    2 & 65 & 12 & 7 & 2 & 0 & 0 & 0  \\ \hline

+    3 & 22 & 1 & 2 & 1 & 0 & 0 & 0  \\ \hline

+    4 & 8 & 0 & 0 & 0 & 0 & 0 & 0  \\ \hline

     5 & 1 & 0 & 0 & 0 & 0 & 0 & 0  \\ \hline

     6 & 1 & 0 & 0 & 0 & 0 & 0 & 0  \\ \hline

   \end{tabular}

@@ -380,11 +380,11 @@ $fg(G)$. В первой колонке указаны возможные зна
   \begin{tabular}{|c|c|c|c|c|c|c|c|c|}

   \hline

     $i(G)$ \textbackslash{} $fg(G)$ & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline

-    1 & 59 & 20 & 8 & 2 & 0 & 0 & 0 & 0  \\ \hline

-    2 & 373 & 129 & 62 & 10 & 0 & 0 & 0 & 0  \\ \hline

-    3 & 210 & 48 & 26 & 1 & 0 & 0 & 0 & 0  \\ \hline

-    4 & 73 & 3 & 7 & 0 & 0 & 0 & 0 & 0  \\ \hline

-    5 & 11 & 0 & 0 & 0 & 0 & 0 & 0 & 0  \\ \hline

+    1 & 95 & 34 & 16 & 6 & 0 & 0 & 0 & 0  \\ \hline

+    2 & 437 & 145 & 72 & 6 & 0 & 0 & 0 & 0  \\ \hline

+    3 & 160 & 21 & 13 & 1 & 0 & 0 & 0 & 0  \\ \hline

+    4 & 28 & 0 & 2 & 0 & 0 & 0 & 0 & 0  \\ \hline

+    5 & 6 & 0 & 0 & 0 & 0 & 0 & 0 & 0  \\ \hline

     6 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0  \\ \hline

     7 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0  \\ \hline

   \end{tabular}

@@ -397,12 +397,12 @@ $fg(G)$. В первой колонке указаны возможные зна
   \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|}

   \hline

     $i(G)$ \textbackslash{} $fg(G)$ & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ \hline

-    1 & 485 & 254 & 93 & 27 & 0 & 0 & 0 & 0 & 0  \\ \hline

-    2 & 4569 & 2059 & 897 & 133 & 1 & 0 & 0 & 0 & 0  \\ \hline

-    3 & 1739 & 555 & 200 & 15 & 2 & 0 & 0 & 0 & 0  \\ \hline

-    4 & 801 & 206 & 78 & 2 & 1 & 0 & 0 & 0 & 0  \\ \hline

-    5 & 183 & 14 & 10 & 0 & 0 & 0 & 0 & 0 & 0  \\ \hline

-    6 & 19 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0  \\ \hline

+    1 & 565 & 299 & 114 & 29 & 0 & 0 & 0 & 0 & 0  \\ \hline

+    2 & 5171 & 2240 & 957 & 134 & 3 & 0 & 0 & 0 & 0  \\ \hline

+    3 & 1749 & 529 & 198 & 12 & 1 & 0 & 0 & 0 & 0  \\ \hline

+    4 & 261 & 21 & 9 & 2 & 0 & 0 & 0 & 0 & 0  \\ \hline

+    5 & 44 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0  \\ \hline

+    6 & 6 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0  \\ \hline

     7 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0  \\ \hline

     8 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0  \\ \hline

   \end{tabular}

@@ -415,13 +415,13 @@ $fg(G)$. В первой колонке указаны возможные зна
   \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|}

   \hline

     $i(G)$ \textbackslash{} $fg(G)$ & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ \hline

-    1 & 6110 & 4128 & 1279 & 379 & 23 & 0 & 0 & 0 & 0 & 0  \\ \hline

-    2 & 108690 & 63700 & 20121 & 3381 & 150 & 0 & 0 & 0 & 0 & 0  \\ \hline

-    3 & 34947 & 18494 & 5062 & 490 & 17 & 0 & 0 & 0 & 0 & 0  \\ \hline

-    4 & 4074 & 1087 & 293 & 22 & 3 & 0 & 0 & 0 & 0 & 0  \\ \hline

-    5 & 1307 & 360 & 84 & 3 & 0 & 0 & 0 & 0 & 0 & 0  \\ \hline

-    6 & 395 & 34 & 8 & 0 & 0 & 0 & 0 & 0 & 0 & 0  \\ \hline

-    7 & 25 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0  \\ \hline

+    1 & 6198 & 4196 & 1310 & 379 & 23 & 0 & 0 & 0 & 0 & 0  \\ \hline

+    2 & 109660 & 64137 & 20190 & 3389 & 150 & 0 & 0 & 0 & 0 & 0  \\ \hline

+    3 & 35432 & 18557 & 5054 & 488 & 19 & 0 & 0 & 0 & 0 & 0  \\ \hline

+    4 & 3744 & 840 & 268 & 19 & 1 & 0 & 0 & 0 & 0 & 0  \\ \hline

+    5 & 437 & 72 & 24 & 0 & 0 & 0 & 0 & 0 & 0 & 0  \\ \hline

+    6 & 70 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0  \\ \hline

+    7 & 7 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0  \\ \hline

     8 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0  \\ \hline

     9 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0  \\ \hline

   \end{tabular}

@@ -434,15 +434,15 @@ $fg(G)$. В первой колонке указаны возможные зна
   \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|}

   \hline

     $i(G)$ \textbackslash{} $fg(G)$ & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ \hline

-    1 & 126042 & 105165 & 25873 & 8402 & 973 & 0 & 0 & 0 & 0 & 0 & 0  \\ \hline

-    2 & 4305543 & 3337594 & 787147 & 164044 & 19062 & 11 & 0 & 0 & 0 & 0 & 0  \\ \hline

-    3 & 1434656 & 1137131 & 237609 & 39140 & 3038 & 3 & 0 & 0 & 0 & 0 & 0  \\ \hline

-    4 & 141618 & 72118 & 15646 & 1907 & 289 & 1 & 0 & 0 & 0 & 0 & 0  \\ \hline

-    5 & 23836 & 12234 & 3025 & 258 & 20 & 0 & 0 & 0 & 0 & 0 & 0  \\ \hline

-    6 & 2065 & 479 & 130 & 4 & 0 & 0 & 0 & 0 & 0 & 0 & 0  \\ \hline

-    7 & 91 & 5 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0  \\ \hline

+    1 & 128633 & 107399 & 26348 & 8563 & 996 & 0 & 0 & 0 & 0 & 0 & 0  \\ \hline

+    2 & 4360884 & 3381726 & 796931 & 165666 & 19278 & 11 & 0 & 0 & 0 & 0 & 0  \\ \hline

+    3 & 1434128 & 1135938 & 237113 & 38740 & 2989 & 3 & 0 & 0 & 0 & 0 & 0  \\ \hline

+    4 & 100512 & 36441 & 8179 & 714 & 113 & 1 & 0 & 0 & 0 & 0 & 0  \\ \hline

+    5 & 8700 & 3023 & 801 & 71 & 6 & 0 & 0 & 0 & 0 & 0 & 0  \\ \hline

+    6 & 947 & 198 & 58 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0  \\ \hline

+    7 & 46 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0  \\ \hline

     8 & 7 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0  \\ \hline

-    9 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0  \\ \hline

+    9 & 2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0  \\ \hline

     10 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0  \\ \hline

   \end{tabular}

   \label{tbl:gr10}

@@ -486,7 +486,7 @@ $G_0 = \set{0, 1, 2}$, $G_1 = \set{3, 4, 5}$).
 

 \begin{figure}[h]

   \centering

-  \begin{tikzpicture}[scale=4]

+  \begin{tikzpicture}[scale=3]

       \draw

         (1.0, 0.0) node[line width=1.5, draw=black, circle] (0){0}

         (0.5, 0.866) node[line width=1.5, draw=black, circle] (1){1}

@@ -510,16 +510,9 @@ $G_0 = \set{0, 1, 2}$, $G_1 = \set{3, 4, 5}$).
   \caption{Визуализация графа <<EFzo>>}

   \label{fig:fg_even}

 \end{figure}

-

-Если $n$ --- нечётное, то $fg(G) = \lfloor \frac{n}{2} \rfloor$ только в том

-случае, если существует два минимальных геодезических

-множества мощности $(\lfloor \frac{n}{2} \rfloor + 1)$, пересекающихся в одной

-вершине (например, рис.

-\ref{fig:fg_odd}, где $G_0 = \set{0, 1, 2, 3}$, $G_1 = \set{0, 4, 5, 6}$).

-

 \begin{figure}[h]

   \centering

-  \begin{tikzpicture}[scale=4]

+  \begin{tikzpicture}[scale=3]

       \draw

         (1.0, 0.0) node[line width=1.5, draw=black, circle] (0){0}

         (0.623, 0.782) node[line width=1.5, draw=black, circle] (1){1}

@@ -548,19 +541,21 @@ $G_0 = \set{0, 1, 2}$, $G_1 = \set{3, 4, 5}$).
   \label{fig:fg_odd}

 \end{figure}

 

+Если $n$ --- нечётное, то $fg(G) = \lfloor \frac{n}{2} \rfloor$ только в том

+случае, если существует два минимальных геодезических

+множества мощности $(\lfloor \frac{n}{2} \rfloor + 1)$, пересекающихся в одной

+вершине (например, рис.

+\ref{fig:fg_odd}, где $G_0 = \set{0, 1, 2, 3}$, $G_1 = \set{0, 4, 5, 6}$).

+

+

 Помимо этого, можно увидеть, что при $fg(G) = 0$ значения $i(G)$ варьируются от

 1 до $n$. Очевидно, что у всех несвязных графов $fg(G) = 0$, поэтому они

 находятся только в этих колонках.

 

-Но при $fg(G) > 0$ значение $i(G) < (n - 2)$ (при $n > 4$).

-Необходимо отметить, что $i(G) = n$ может быть только в случае, если граф

-пустой. Но в пустом графе не может быть $fg(G) > 0$. Поэтому $i(G) = n$ и

-$fg(G) > 0$ не может быть ни у одного графа. $i(G) = 1$ при этом может быть

-только у полного графа. Но у полного графа минимальными геодезическими

-множествами являются любые две пары вершин. То есть ни в одной из таких пар нет

-уникальной вершины, находящейся только в этой паре. Таким образом, $fg(G) = 0$.

-Для всех остальных графов не может быть справедливо одновременно $i(G) = 1$ и

-$fg(G) > 0$.

+Но при $fg(G) > 0$ значение $i(G) < (n - 2)$ (при $n > 4$). Необходимо

+отметить, что $i(G) = n$ может быть только в случае, если граф пустой. Но в

+пустом графе не может быть $fg(G) > 0$. Поэтому $i(G) = n$ и $fg(G) > 0$ не

+может быть ни у одного графа.

 

 Рассмотрим случай с $i(G) = n - 2$. Получаем, что существует $n - 2$ вершины

 (обозначим множеством $V_i$), не смежные между собой и каждая из них смежна

@@ -612,9 +607,8 @@ $fg(G)$.
         \draw[line width=1.5] (1) to (3);

       \end{scope}

     \end{tikzpicture}

-  \caption{Визуализация графа <<C]>>, $i(G) = 2, fg(G) = 2$}

+  \caption{Визуализация графа <<C]>>, $i(G) = 2$, $fg(G) = 2$}

 \end{figure}

-

 \begin{figure}[h]

   \centering

   \begin{tikzpicture}[scale=4]

@@ -635,9 +629,8 @@ $fg(G)$.
         \draw[line width=1.5] (3) to (4);

       \end{scope}

     \end{tikzpicture}

-  \caption{Визуализация графа <<D]\{>>, $i(G) = 2, fg(G) = 2$}

+  \caption{Визуализация графа <<D]\{>>, $i(G) = 1$, $fg(G) = 2$}

 \end{figure}

-

 \begin{figure}[h]

   \centering

   \begin{tikzpicture}[scale=4]

@@ -656,9 +649,8 @@ $fg(G)$.
         \draw[line width=1.5] (4) to (5);

       \end{scope}

     \end{tikzpicture}

-  \caption{Визуализация графа <<E?bg>>, $i(G) = 4, fg(G) = 0$}

+  \caption{Визуализация графа <<E?bg>>, $i(G) = 2$, $fg(G) = 0$}

 \end{figure}

-

 \begin{figure}[h]

   \centering

   \begin{tikzpicture}[scale=4]

@@ -678,9 +670,8 @@ $fg(G)$.
         \draw[line width=1.5] (3) to (5);

       \end{scope}

     \end{tikzpicture}

-  \caption{Визуализация графа <<ECpo>>, $i(G) = 3, fg(G) = 1$}

+  \caption{Визуализация графа <<ECpo>>, $i(G) = 2$, $fg(G) = 1$}

 \end{figure}

-

 \begin{figure}[h]

   \centering

   \begin{tikzpicture}[scale=4]

@@ -705,9 +696,8 @@ $fg(G)$.
         \draw[line width=1.5] (5) to (6);

       \end{scope}

     \end{tikzpicture}

-  \caption{Визуализация графа <<F?rdw>>, $i(G) = 4, fg(G) = 2$}

+  \caption{Визуализация графа <<F?rdw>>, $i(G) = 4$, $fg(G) = 2$}

 \end{figure}

-

 \begin{figure}[h]

   \centering

   \begin{tikzpicture}[scale=4]

@@ -743,9 +733,8 @@ $fg(G)$.
         \draw[line width=1.5] (5) to (6);

       \end{scope}

     \end{tikzpicture}

-  \caption{Визуализация графа <<F~~~w>>, $i(G) = 1, fg(G) = 0$}

+  \caption{Визуализация графа <<F~~~w>>, $i(G) = 1$, $fg(G) = 0$}

 \end{figure}

-

 \begin{figure}[h]

   \centering

   \begin{tikzpicture}[scale=4]

@@ -759,21 +748,13 @@ $fg(G)$.
         (0.0, -1.0) node[line width=1.5, draw=black, circle] (6){6}

         (0.707, -0.707) node[line width=1.5, draw=black, circle] (7){7};

       \begin{scope}[-]

-        \draw[line width=1.5] (0) to (4);

-        \draw[line width=1.5] (0) to (5);

-        \draw[line width=1.5] (1) to (4);

+        \draw[line width=1.5] (0) to (7);

         \draw[line width=1.5] (1) to (7);

-        \draw[line width=1.5] (2) to (5);

-        \draw[line width=1.5] (2) to (6);

-        \draw[line width=1.5] (3) to (6);

-        \draw[line width=1.5] (3) to (7);

-        \draw[line width=1.5] (4) to (6);

-        \draw[line width=1.5] (5) to (7);

+        \draw[line width=1.5] (2) to (7);

       \end{scope}

     \end{tikzpicture}

-  \caption{Визуализация графа <<G?q`qg>>, $i(G) = 4, fg(G) = 4$}

+  \caption{Визуализация графа <<G???F?>>, $i(G) = 5$, $fg(G) = 0$}

 \end{figure}

-

 \begin{figure}[h]

   \centering

   \begin{tikzpicture}[scale=4]

@@ -787,24 +768,17 @@ $fg(G)$.
         (0.0, -1.0) node[line width=1.5, draw=black, circle] (6){6}

         (0.707, -0.707) node[line width=1.5, draw=black, circle] (7){7};

       \begin{scope}[-]

-        \draw[line width=1.5] (0) to (3);

         \draw[line width=1.5] (0) to (5);

         \draw[line width=1.5] (0) to (6);

-        \draw[line width=1.5] (1) to (4);

-        \draw[line width=1.5] (1) to (5);

         \draw[line width=1.5] (1) to (6);

-        \draw[line width=1.5] (2) to (5);

+        \draw[line width=1.5] (1) to (7);

         \draw[line width=1.5] (2) to (6);

-        \draw[line width=1.5] (2) to (7);

-        \draw[line width=1.5] (3) to (5);

         \draw[line width=1.5] (3) to (7);

-        \draw[line width=1.5] (4) to (6);

         \draw[line width=1.5] (4) to (7);

         \draw[line width=1.5] (5) to (7);

-        \draw[line width=1.5] (6) to (7);

       \end{scope}

     \end{tikzpicture}

-  \caption{Визуализация графа <<GCRvP\{>>, $i(G) = 3, fg(G) = 4$}

+  \caption{Визуализация графа <<G?AFAw>>, $i(G) = 2$, $fg(G) = 1$}

 \end{figure}

 

 \begin{figure}[h]

@@ -820,22 +794,19 @@ $fg(G)$.
         (0.0, -1.0) node[line width=1.5, draw=black, circle] (6){6}

         (0.707, -0.707) node[line width=1.5, draw=black, circle] (7){7};

       \begin{scope}[-]

-        \draw[line width=1.5] (0) to (3);

-        \draw[line width=1.5] (0) to (6);

-        \draw[line width=1.5] (0) to (7);

+        \draw[line width=1.5] (0) to (4);

+        \draw[line width=1.5] (0) to (5);

         \draw[line width=1.5] (1) to (4);

-        \draw[line width=1.5] (1) to (6);

         \draw[line width=1.5] (1) to (7);

         \draw[line width=1.5] (2) to (5);

         \draw[line width=1.5] (2) to (6);

-        \draw[line width=1.5] (2) to (7);

         \draw[line width=1.5] (3) to (6);

         \draw[line width=1.5] (3) to (7);

         \draw[line width=1.5] (4) to (6);

         \draw[line width=1.5] (5) to (7);

       \end{scope}

     \end{tikzpicture}

-  \caption{Визуализация графа <<GCOfvg>>, $i(G) = 3, fg(G) = 2$}

+  \caption{Визуализация графа <<G?q`qg>>, $i(G) = 3$, $fg(G) = 4$}

 \end{figure}

 

 \begin{figure}[h]

@@ -851,14 +822,23 @@ $fg(G)$.
         (0.0, -1.0) node[line width=1.5, draw=black, circle] (6){6}

         (0.707, -0.707) node[line width=1.5, draw=black, circle] (7){7};

       \begin{scope}[-]

+        \draw[line width=1.5] (0) to (3);

+        \draw[line width=1.5] (0) to (6);

         \draw[line width=1.5] (0) to (7);

+        \draw[line width=1.5] (1) to (4);

+        \draw[line width=1.5] (1) to (6);

         \draw[line width=1.5] (1) to (7);

+        \draw[line width=1.5] (2) to (5);

+        \draw[line width=1.5] (2) to (6);

         \draw[line width=1.5] (2) to (7);

+        \draw[line width=1.5] (3) to (6);

+        \draw[line width=1.5] (3) to (7);

+        \draw[line width=1.5] (4) to (6);

+        \draw[line width=1.5] (5) to (7);

       \end{scope}

     \end{tikzpicture}

-  \caption{Визуализация графа <<G???F?>>, $i(G) = 7, fg(G) = 0$}

+  \caption{Визуализация графа <<GCOfvg>>, $i(G) = 2$, $fg(G) = 2$}

 \end{figure}

-

 \begin{figure}[h]

   \centering

   \begin{tikzpicture}[scale=4]

@@ -872,19 +852,25 @@ $fg(G)$.
         (0.0, -1.0) node[line width=1.5, draw=black, circle] (6){6}

         (0.707, -0.707) node[line width=1.5, draw=black, circle] (7){7};

       \begin{scope}[-]

+        \draw[line width=1.5] (0) to (3);

         \draw[line width=1.5] (0) to (5);

         \draw[line width=1.5] (0) to (6);

+        \draw[line width=1.5] (1) to (4);

+        \draw[line width=1.5] (1) to (5);

         \draw[line width=1.5] (1) to (6);

-        \draw[line width=1.5] (1) to (7);

+        \draw[line width=1.5] (2) to (5);

         \draw[line width=1.5] (2) to (6);

+        \draw[line width=1.5] (2) to (7);

+        \draw[line width=1.5] (3) to (5);

         \draw[line width=1.5] (3) to (7);

+        \draw[line width=1.5] (4) to (6);

         \draw[line width=1.5] (4) to (7);

         \draw[line width=1.5] (5) to (7);

+        \draw[line width=1.5] (6) to (7);

       \end{scope}

     \end{tikzpicture}

-  \caption{Визуализация графа <<G?AFAw>>, $i(G) = 5, fg(G) = 1$}

+  \caption{Визуализация графа <<GCRvP\{>>, $i(G) = 2$, $fg(G) = 4$}

 \end{figure}

-

 \begin{figure}[h]

   \centering

   \begin{tikzpicture}[scale=4]

@@ -899,38 +885,25 @@ $fg(G)$.
         (0.174, -0.985) node[line width=1.5, draw=black, circle] (7){7}

         (0.766, -0.643) node[line width=1.5, draw=black, circle] (8){8};

       \begin{scope}[-]

-        \draw[line width=1.5] (0) to (2);

-        \draw[line width=1.5] (0) to (4);

-        \draw[line width=1.5] (0) to (5);

         \draw[line width=1.5] (0) to (6);

         \draw[line width=1.5] (0) to (7);

         \draw[line width=1.5] (0) to (8);

-        \draw[line width=1.5] (1) to (3);

-        \draw[line width=1.5] (1) to (4);

-        \draw[line width=1.5] (1) to (6);

         \draw[line width=1.5] (1) to (7);

         \draw[line width=1.5] (1) to (8);

-        \draw[line width=1.5] (2) to (4);

-        \draw[line width=1.5] (2) to (5);

-        \draw[line width=1.5] (2) to (6);

         \draw[line width=1.5] (2) to (7);

         \draw[line width=1.5] (2) to (8);

-        \draw[line width=1.5] (3) to (5);

-        \draw[line width=1.5] (3) to (6);

         \draw[line width=1.5] (3) to (7);

-        \draw[line width=1.5] (4) to (5);

-        \draw[line width=1.5] (4) to (6);

+        \draw[line width=1.5] (3) to (8);

+        \draw[line width=1.5] (4) to (7);

         \draw[line width=1.5] (4) to (8);

         \draw[line width=1.5] (5) to (7);

         \draw[line width=1.5] (5) to (8);

-        \draw[line width=1.5] (6) to (7);

         \draw[line width=1.5] (6) to (8);

         \draw[line width=1.5] (7) to (8);

       \end{scope}

     \end{tikzpicture}

-  \caption{Визуализация графа <<HQy~vnn>>, $i(G) = 2, fg(G) = 3$}

+  \caption{Визуализация графа <<H??CFz~>>, $i(G) = 1$, $fg(G) = 1$}

 \end{figure}

-

 \begin{figure}[h]

   \centering

   \begin{tikzpicture}[scale=4]

@@ -965,9 +938,8 @@ $fg(G)$.
         \draw[line width=1.5] (7) to (8);

       \end{scope}

     \end{tikzpicture}

-  \caption{Визуализация графа <<HQhTVbd>>, $i(G) = 2, fg(G) = 2$}

+  \caption{Визуализация графа <<HQhTVbd>>, $i(G) = 2$, $fg(G) = 2$}

 \end{figure}

-

 \begin{figure}[h]

   \centering

   \begin{tikzpicture}[scale=4]

@@ -982,26 +954,37 @@ $fg(G)$.
         (0.174, -0.985) node[line width=1.5, draw=black, circle] (7){7}

         (0.766, -0.643) node[line width=1.5, draw=black, circle] (8){8};

       \begin{scope}[-]

+        \draw[line width=1.5] (0) to (2);

+        \draw[line width=1.5] (0) to (4);

+        \draw[line width=1.5] (0) to (5);

         \draw[line width=1.5] (0) to (6);

         \draw[line width=1.5] (0) to (7);

         \draw[line width=1.5] (0) to (8);

+        \draw[line width=1.5] (1) to (3);

+        \draw[line width=1.5] (1) to (4);

+        \draw[line width=1.5] (1) to (6);

         \draw[line width=1.5] (1) to (7);

         \draw[line width=1.5] (1) to (8);

+        \draw[line width=1.5] (2) to (4);

+        \draw[line width=1.5] (2) to (5);

+        \draw[line width=1.5] (2) to (6);

         \draw[line width=1.5] (2) to (7);

         \draw[line width=1.5] (2) to (8);

+        \draw[line width=1.5] (3) to (5);

+        \draw[line width=1.5] (3) to (6);

         \draw[line width=1.5] (3) to (7);

-        \draw[line width=1.5] (3) to (8);

-        \draw[line width=1.5] (4) to (7);

+        \draw[line width=1.5] (4) to (5);

+        \draw[line width=1.5] (4) to (6);

         \draw[line width=1.5] (4) to (8);

         \draw[line width=1.5] (5) to (7);

         \draw[line width=1.5] (5) to (8);

+        \draw[line width=1.5] (6) to (7);

         \draw[line width=1.5] (6) to (8);

         \draw[line width=1.5] (7) to (8);

       \end{scope}

     \end{tikzpicture}

-  \caption{Визуализация графа <<H??CFz~>>, $i(G) = 6, fg(G) = 1$}

+  \caption{Визуализация графа <<HQy~vnn>>, $i(G) = 2$, $fg(G) = 3$}

 \end{figure}

-

 \begin{figure}[h]

   \centering

   \begin{tikzpicture}[scale=4]

@@ -1019,9 +1002,8 @@ $fg(G)$.
       \begin{scope}[-]

       \end{scope}

     \end{tikzpicture}

-  \caption{Визуализация графа <<I????????>>, $i(G) = 10, fg(G) = 0$}

+  \caption{Визуализация графа <<I????????>>, $i(G) = 10$, $fg(G) = 0$}

 \end{figure}

-

 \begin{figure}[h]

   \centering

   \begin{tikzpicture}[scale=4]

@@ -1037,25 +1019,23 @@ $fg(G)$.
         (0.309, -0.951) node[line width=1.5, draw=black, circle] (8){8}

         (0.809, -0.588) node[line width=1.5, draw=black, circle] (9){9};

       \begin{scope}[-]

-        \draw[line width=1.5] (0) to (5);

-        \draw[line width=1.5] (0) to (6);

         \draw[line width=1.5] (0) to (7);

-        \draw[line width=1.5] (1) to (5);

+        \draw[line width=1.5] (0) to (8);

+        \draw[line width=1.5] (0) to (9);

+        \draw[line width=1.5] (1) to (7);

         \draw[line width=1.5] (1) to (8);

-        \draw[line width=1.5] (2) to (6);

-        \draw[line width=1.5] (2) to (7);

-        \draw[line width=1.5] (2) to (8);

-        \draw[line width=1.5] (3) to (8);

-        \draw[line width=1.5] (5) to (7);

+        \draw[line width=1.5] (1) to (9);

+        \draw[line width=1.5] (2) to (9);

+        \draw[line width=1.5] (3) to (9);

+        \draw[line width=1.5] (4) to (9);

         \draw[line width=1.5] (5) to (9);

         \draw[line width=1.5] (6) to (9);

         \draw[line width=1.5] (7) to (9);

         \draw[line width=1.5] (8) to (9);

       \end{scope}

     \end{tikzpicture}

-  \caption{Визуализация графа <<I?BDDHo@w>>, $i(G) = 4, fg(G) = 0$}

+  \caption{Визуализация графа <<I???EB?~w>>, $i(G) = 1$, $fg(G) = 2$}

 \end{figure}

-

 \begin{figure}[h]

   \centering

   \begin{tikzpicture}[scale=4]

@@ -1071,25 +1051,25 @@ $fg(G)$.
         (0.309, -0.951) node[line width=1.5, draw=black, circle] (8){8}

         (0.809, -0.588) node[line width=1.5, draw=black, circle] (9){9};

       \begin{scope}[-]

-        \draw[line width=1.5] (0) to (5);

-        \draw[line width=1.5] (0) to (7);

+        \draw[line width=1.5] (0) to (6);

         \draw[line width=1.5] (0) to (8);

-        \draw[line width=1.5] (1) to (5);

+        \draw[line width=1.5] (1) to (7);

         \draw[line width=1.5] (1) to (8);

-        \draw[line width=1.5] (2) to (6);

-        \draw[line width=1.5] (3) to (6);

-        \draw[line width=1.5] (4) to (7);

+        \draw[line width=1.5] (2) to (8);

+        \draw[line width=1.5] (2) to (9);

+        \draw[line width=1.5] (3) to (8);

+        \draw[line width=1.5] (3) to (9);

         \draw[line width=1.5] (4) to (8);

-        \draw[line width=1.5] (5) to (7);

+        \draw[line width=1.5] (4) to (9);

+        \draw[line width=1.5] (5) to (8);

         \draw[line width=1.5] (5) to (9);

         \draw[line width=1.5] (6) to (9);

         \draw[line width=1.5] (7) to (9);

         \draw[line width=1.5] (8) to (9);

       \end{scope}

     \end{tikzpicture}

-  \caption{Визуализация графа <<I?B@cZG@w>>, $i(G) = 4, fg(G) = 1$}

+  \caption{Визуализация графа <<I??CAB\{Nw>>, $i(G) = 3$, $fg(G) = 2$}

 \end{figure}

-

 \begin{figure}[h]

   \centering

   \begin{tikzpicture}[scale=4]

@@ -1105,33 +1085,20 @@ $fg(G)$.
         (0.309, -0.951) node[line width=1.5, draw=black, circle] (8){8}

         (0.809, -0.588) node[line width=1.5, draw=black, circle] (9){9};

       \begin{scope}[-]

-        \draw[line width=1.5] (0) to (3);

-        \draw[line width=1.5] (0) to (6);

-        \draw[line width=1.5] (0) to (7);

+        \draw[line width=1.5] (0) to (5);

         \draw[line width=1.5] (0) to (8);

-        \draw[line width=1.5] (1) to (4);

-        \draw[line width=1.5] (1) to (5);

         \draw[line width=1.5] (1) to (6);

-        \draw[line width=1.5] (1) to (7);

-        \draw[line width=1.5] (2) to (4);

-        \draw[line width=1.5] (2) to (5);

+        \draw[line width=1.5] (1) to (8);

+        \draw[line width=1.5] (1) to (9);

         \draw[line width=1.5] (2) to (7);

-        \draw[line width=1.5] (2) to (8);

-        \draw[line width=1.5] (3) to (6);

+        \draw[line width=1.5] (2) to (9);

         \draw[line width=1.5] (3) to (8);

-        \draw[line width=1.5] (4) to (5);

-        \draw[line width=1.5] (4) to (7);

         \draw[line width=1.5] (4) to (9);

         \draw[line width=1.5] (5) to (9);

-        \draw[line width=1.5] (6) to (8);

-        \draw[line width=1.5] (6) to (9);

-        \draw[line width=1.5] (7) to (9);

-        \draw[line width=1.5] (8) to (9);

       \end{scope}

     \end{tikzpicture}

-  \caption{Визуализация графа <<ICXmfQqBw>>, $i(G) = 2, fg(G) = 1$}

+  \caption{Визуализация графа <<I?AA@BOZ?>>, $i(G) = 4$, $fg(G) = 1$}

 \end{figure}

-

 \begin{figure}[h]

   \centering

   \begin{tikzpicture}[scale=4]

@@ -1148,20 +1115,29 @@ $fg(G)$.
         (0.809, -0.588) node[line width=1.5, draw=black, circle] (9){9};

       \begin{scope}[-]

         \draw[line width=1.5] (0) to (5);

-        \draw[line width=1.5] (0) to (8);

+        \draw[line width=1.5] (0) to (7);

+        \draw[line width=1.5] (0) to (9);

         \draw[line width=1.5] (1) to (6);

+        \draw[line width=1.5] (1) to (7);

         \draw[line width=1.5] (1) to (8);

         \draw[line width=1.5] (1) to (9);

-        \draw[line width=1.5] (2) to (7);

+        \draw[line width=1.5] (2) to (6);

+        \draw[line width=1.5] (2) to (8);

         \draw[line width=1.5] (2) to (9);

-        \draw[line width=1.5] (3) to (8);

+        \draw[line width=1.5] (3) to (7);

+        \draw[line width=1.5] (3) to (9);

+        \draw[line width=1.5] (4) to (8);

         \draw[line width=1.5] (4) to (9);

+        \draw[line width=1.5] (5) to (8);

         \draw[line width=1.5] (5) to (9);

+        \draw[line width=1.5] (6) to (7);

+        \draw[line width=1.5] (6) to (9);

+        \draw[line width=1.5] (7) to (8);

+        \draw[line width=1.5] (8) to (9);

       \end{scope}

     \end{tikzpicture}

-  \caption{Визуализация графа <<I?AA@BOZ?>>, $i(G) = 5, fg(G) = 1$}

+  \caption{Визуализация графа <<I?ABEdl~g>>, $i(G) = 2$, $fg(G) = 4$}

 \end{figure}

-

 \begin{figure}[h]

   \centering

   \begin{tikzpicture}[scale=4]

@@ -1178,30 +1154,23 @@ $fg(G)$.
         (0.809, -0.588) node[line width=1.5, draw=black, circle] (9){9};

       \begin{scope}[-]

         \draw[line width=1.5] (0) to (5);

+        \draw[line width=1.5] (0) to (6);

         \draw[line width=1.5] (0) to (7);

-        \draw[line width=1.5] (0) to (9);

-        \draw[line width=1.5] (1) to (6);

-        \draw[line width=1.5] (1) to (7);

+        \draw[line width=1.5] (1) to (5);

         \draw[line width=1.5] (1) to (8);

-        \draw[line width=1.5] (1) to (9);

         \draw[line width=1.5] (2) to (6);

+        \draw[line width=1.5] (2) to (7);

         \draw[line width=1.5] (2) to (8);

-        \draw[line width=1.5] (2) to (9);

-        \draw[line width=1.5] (3) to (7);

-        \draw[line width=1.5] (3) to (9);

-        \draw[line width=1.5] (4) to (8);

-        \draw[line width=1.5] (4) to (9);

-        \draw[line width=1.5] (5) to (8);

+        \draw[line width=1.5] (3) to (8);

+        \draw[line width=1.5] (5) to (7);

         \draw[line width=1.5] (5) to (9);

-        \draw[line width=1.5] (6) to (7);

         \draw[line width=1.5] (6) to (9);

-        \draw[line width=1.5] (7) to (8);

+        \draw[line width=1.5] (7) to (9);

         \draw[line width=1.5] (8) to (9);

       \end{scope}

     \end{tikzpicture}

-  \caption{Визуализация графа <<I?ABEdl~g>>, $i(G) = 5, fg(G) = 4$}

+  \caption{Визуализация графа <<I?BDDHo@w>>, $i(G) = 3$, $fg(G) = 0$}

 \end{figure}

-

 \begin{figure}[h]

   \centering

   \begin{tikzpicture}[scale=4]

@@ -1218,30 +1187,23 @@ $fg(G)$.
         (0.809, -0.588) node[line width=1.5, draw=black, circle] (9){9};

       \begin{scope}[-]

         \draw[line width=1.5] (0) to (5);

-        \draw[line width=1.5] (0) to (6);

+        \draw[line width=1.5] (0) to (7);

         \draw[line width=1.5] (0) to (8);

         \draw[line width=1.5] (1) to (5);

-        \draw[line width=1.5] (1) to (7);

         \draw[line width=1.5] (1) to (8);

-        \draw[line width=1.5] (2) to (5);

-        \draw[line width=1.5] (2) to (7);

-        \draw[line width=1.5] (2) to (9);

+        \draw[line width=1.5] (2) to (6);

         \draw[line width=1.5] (3) to (6);

-        \draw[line width=1.5] (3) to (7);

-        \draw[line width=1.5] (3) to (9);

-        \draw[line width=1.5] (4) to (6);

+        \draw[line width=1.5] (4) to (7);

         \draw[line width=1.5] (4) to (8);

-        \draw[line width=1.5] (4) to (9);

         \draw[line width=1.5] (5) to (7);

-        \draw[line width=1.5] (5) to (8);

-        \draw[line width=1.5] (6) to (8);

+        \draw[line width=1.5] (5) to (9);

         \draw[line width=1.5] (6) to (9);

         \draw[line width=1.5] (7) to (9);

+        \draw[line width=1.5] (8) to (9);

       \end{scope}

     \end{tikzpicture}

-  \caption{Визуализация графа <<I?BcrjMMo>>, $i(G) = 5, fg(G) = 5$}

+  \caption{Визуализация графа <<I?B@cZG@w>>, $i(G) = 3$, $fg(G) = 1$}

 \end{figure}

-

 \begin{figure}[h]

   \centering

   \begin{tikzpicture}[scale=4]

@@ -1257,24 +1219,30 @@ $fg(G)$.
         (0.309, -0.951) node[line width=1.5, draw=black, circle] (8){8}

         (0.809, -0.588) node[line width=1.5, draw=black, circle] (9){9};

       \begin{scope}[-]

-        \draw[line width=1.5] (0) to (7);

+        \draw[line width=1.5] (0) to (5);

+        \draw[line width=1.5] (0) to (6);

         \draw[line width=1.5] (0) to (8);

-        \draw[line width=1.5] (0) to (9);

+        \draw[line width=1.5] (1) to (5);

         \draw[line width=1.5] (1) to (7);

         \draw[line width=1.5] (1) to (8);

-        \draw[line width=1.5] (1) to (9);

+        \draw[line width=1.5] (2) to (5);

+        \draw[line width=1.5] (2) to (7);

         \draw[line width=1.5] (2) to (9);

+        \draw[line width=1.5] (3) to (6);

+        \draw[line width=1.5] (3) to (7);

         \draw[line width=1.5] (3) to (9);

+        \draw[line width=1.5] (4) to (6);

+        \draw[line width=1.5] (4) to (8);

         \draw[line width=1.5] (4) to (9);

-        \draw[line width=1.5] (5) to (9);

+        \draw[line width=1.5] (5) to (7);

+        \draw[line width=1.5] (5) to (8);

+        \draw[line width=1.5] (6) to (8);

         \draw[line width=1.5] (6) to (9);

         \draw[line width=1.5] (7) to (9);

-        \draw[line width=1.5] (8) to (9);

       \end{scope}

     \end{tikzpicture}

-  \caption{Визуализация графа <<I???EB?~w>>, $i(G) = 7, fg(G) = 2$}

+  \caption{Визуализация графа <<I?BcrjMMo>>, $i(G) = 2$, $fg(G) = 5$}

 \end{figure}

-

 \begin{figure}[h]

   \centering

   \begin{tikzpicture}[scale=4]

@@ -1290,26 +1258,32 @@ $fg(G)$.
         (0.309, -0.951) node[line width=1.5, draw=black, circle] (8){8}

         (0.809, -0.588) node[line width=1.5, draw=black, circle] (9){9};

       \begin{scope}[-]

+        \draw[line width=1.5] (0) to (3);

         \draw[line width=1.5] (0) to (6);

+        \draw[line width=1.5] (0) to (7);

         \draw[line width=1.5] (0) to (8);

+        \draw[line width=1.5] (1) to (4);

+        \draw[line width=1.5] (1) to (5);

+        \draw[line width=1.5] (1) to (6);

         \draw[line width=1.5] (1) to (7);

-        \draw[line width=1.5] (1) to (8);

+        \draw[line width=1.5] (2) to (4);

+        \draw[line width=1.5] (2) to (5);

+        \draw[line width=1.5] (2) to (7);

         \draw[line width=1.5] (2) to (8);

-        \draw[line width=1.5] (2) to (9);

+        \draw[line width=1.5] (3) to (6);

         \draw[line width=1.5] (3) to (8);

-        \draw[line width=1.5] (3) to (9);

-        \draw[line width=1.5] (4) to (8);

+        \draw[line width=1.5] (4) to (5);

+        \draw[line width=1.5] (4) to (7);

         \draw[line width=1.5] (4) to (9);

-        \draw[line width=1.5] (5) to (8);

         \draw[line width=1.5] (5) to (9);

+        \draw[line width=1.5] (6) to (8);

         \draw[line width=1.5] (6) to (9);

         \draw[line width=1.5] (7) to (9);

         \draw[line width=1.5] (8) to (9);

       \end{scope}

     \end{tikzpicture}

-  \caption{Визуализация графа <<I??CAB\{Nw>>, $i(G) = 6, fg(G) = 2$}

+  \caption{Визуализация графа <<ICXmfQqBw>>, $i(G) = 2$, $fg(G) = 1$}

 \end{figure}

-

 \begin{figure}[h]

   \centering

   \begin{tikzpicture}[scale=4]

@@ -1353,7 +1327,7 @@ $fg(G)$.
         \draw[line width=1.5] (8) to (9);

       \end{scope}

     \end{tikzpicture}

-  \caption{Визуализация графа <<IEhuTxyFw>>, $i(G) = 2, fg(G) = 3$}

+  \caption{Визуализация графа <<IEhuTxyFw>>, $i(G) = 2$, $fg(G) = 3$}

 \end{figure}

 

 \conclusion