Задание №2
Задание:
В заданном графе Gk определить все пути длиной λ=2.
Решение:
Возведем матрицу А в квадрат (т.к. λ=2):
А2=А*А=
|
X1 |
X2 |
X3 |
X4 |
X5 |
X6 |
X7 |
X8 |
X9 |
X10 |
X11 |
X12 |
X13 |
X1 |
0 |
0 |
0 |
1 |
2 |
1 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
X2 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
2 |
1 |
0 |
1 |
0 |
0 |
X3 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
2 |
2 |
2 |
1 |
0 |
0 |
X4 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
1 |
X5 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
0 |
X6 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
X7 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
2 |
2 |
0 |
X8 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
X9 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
X10 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
2 |
X11 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
X12 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
X13 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
Пути длиной 2:
x1x2x4; x1x2x5 ; x1x3x4 ; x1x3x6 ; x1x3x7 ; x2x5x8 ; x2x4x8 ; x2x5x9 ; x2x4x11 ; x3x5x8 ; x3x7x8; x3x7x9; x3x5x9; x3x7x10; x3x6x10; x3x6x11; x4x8x11; x4x11x13; x5x8x11; x5x9x12; x6x10x11; x6x10x12; x6x11x13; x7x10x11; x7x8x11; x7x10x12; x7x9x12; x8x11x13; x9x12x13; x10x12x13; x10x11x13.
Задание №3
Задание:
Для заданного графа Gk построить конденсацию и определить базы и
антибазы.
Решение:
Достижимость:
R=
|
X1 |
X2 |
X3 |
X4 |
X5 |
X6 |
X7 |
X8 |
X9 |
X10 |
X11 |
X12 |
X13 |
X1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
X2 |
0 |
1 |
0 |
1 |
1 |
0 |
0 |
1 |
1 |
0 |
1 |
1 |
1 |
X3 |
0 |
0 |
1 |
0 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
X4 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
1 |
0 |
0 |
1 |
0 |
1 |
X5 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
1 |
1 |
0 |
1 |
1 |
1 |
X6 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
X7 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
X8 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
1 |
0 |
1 |
X9 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
1 |
1 |
X10 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
0 |
X11 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
1 |
X12 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
X13 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |