3. Графы
1. Изобразить граф, заданный матрицей смежности. Определить, является ли граф планарным, записать образы и прообразы всех вершин графа, найти степени вершин. Составить матрицу инцидентности и связности (сильной связности).
2. Найти минимальный путь из x1 в x7 в ориентированном графе, заданном матрицей весов.
3. Найти минимальное остовное дерево для графа, заданного матрицей длин ребер.
Варианты индивидуальных заданий
Вариант
№ 1
1
.
0 1 1 0 1 1 2. ¥
4 6 12 ¥ ¥
¥ 3. ¥
12 6 20 14
1 0 0 1 0 0 ¥ ¥ ¥ 13 7 ¥ ¥ 12 ¥ 2 4 6
1 0 0 0 1 0 ¥ ¥ ¥ 5 ¥ 3 ¥ 6 2 ¥ 10 12
0 1 0 0 1 0 ¥ ¥ ¥ ¥ 10 9 ¥ 20 4 10 ¥ 6
1 0 1 1 0 1 ¥ ¥ ¥ ¥ ¥ ¥ 8 14 6 12 6 ¥
1 0 0 0 1 0 ¥ ¥ ¥ ¥ ¥ ¥ 11
¥ ¥ ¥ ¥ ¥ ¥ ¥
В
ариант
№ 2
1
.
0 0 0 0 0 1 2. ¥
1 3 9 ¥ ¥
¥ 3. ¥
1 ¥ 4 5
0 0 1 1 1 0 ¥ ¥ ¥ 10 4 ¥ ¥ 1 ¥ 2 ¥ 1
0 0 0 0 0 0 ¥ ¥ ¥ 2 ¥ 1 ¥ ¥ 2 ¥ 1 1
1 0 0 0 0 1 ¥ ¥ ¥ ¥ 7 6 ¥ 4 ¥ 1 ¥ 3
1 0 1 0 0 0 ¥ ¥ ¥ ¥ ¥ ¥ 5 5 1 1 3 ¥
1 0 1 0 0 0 ¥ ¥ ¥ ¥ ¥ ¥ 8
¥ ¥ ¥ ¥ ¥ ¥ ¥
Вариант № 3
1
.
0 1 0 1 0 0 2. ¥
3 5 11 ¥ ¥
¥ 3. ¥
6 3 10 7
1 0 0 1 0 0 ¥ ¥ ¥ 12 6 ¥ ¥ 6 ¥ 1 2 3
0 0 0 0 1 1 ¥ ¥ ¥ 3 ¥ 2 ¥ 3 1 ¥ 5 6
1 1 0 0 1 1 ¥ ¥ ¥ ¥ 9 8 ¥ 10 2 5 ¥ 3
0 0 1 1 0 0 ¥ ¥ ¥ ¥ ¥ ¥ 7 7 3 6 3 ¥
0 0 1 1 0 0 ¥ ¥ ¥ ¥ ¥ ¥ 10
¥ ¥ ¥ ¥ ¥ ¥ ¥
Вариант № 4
1
.
0 0 0 0 0 1 2. ¥
¥ 5 4 2 2 9
3. ¥ 7 2 11 7
1 0 1 0 1 1 ¥ ¥ 1 1 ¥ 1 1 7 ¥ 3 ¥ 4
1 0 0 0 0 0 2 ¥ ¥ 1 1 ¥ 3 2 3 ¥ 1 5
0 0 1 0 0 1 ¥ 2 1 ¥ 1 ¥ ¥ 11 ¥ 1 ¥ 3
0 1 1 1 0 0 ¥ ¥ 2 2 ¥ 1 6 7 4 5 3 ¥
0 0 1 0 0 0 1 5 ¥ 1 1 ¥ ¥
2 ¥ 1 ¥ 1 2 ¥
Вариант № 5
1
.
0 0 0 1 1 0 2. ¥
4 ¥ ¥
3 1 ¥ 3.
¥ 2 ¥
5 5
0 0 0 1 0 1 3 ¥ 2 1 ¥ ¥ 4 2 ¥ 8 ¥ 7
1 0 0 0 0 0 1 1 ¥ ¥ ¥ ¥ 1 ¥ 8 ¥ 10 1
0 1 0 0 0 1 ¥ 3 1 ¥ 1 ¥ ¥ 5 ¥ 10 ¥ 13
1 0 0 0 0 0 ¥ ¥ 2 ¥ ¥ 1 5 5 7 1 13 ¥
0 1 0 1 0 0 ¥ 3 ¥ 2 2 ¥ ¥
¥ ¥ 2 ¥ ¥ 2 ¥
В
ариант
№ 6
1
.
0 0 1 0 1 0 2. ¥
¥ 9 ¥
¥ 2 12 3. ¥
1 5 4 5
0 0 1 1 1 1 1 ¥ ¥ ¥ 1 2 4 1 ¥ 2 6 1
1 1 0 0 1 0 2 1 ¥ ¥ 1 ¥ 2 5 2 ¥ 1 7
0 1 0 0 0 1 ¥ 1 1 ¥ ¥ 1 ¥ 4 6 1 ¥ 4
1 1 1 0 0 0 1 2 ¥ 2 ¥ ¥ ¥ 5 1 7 4 ¥
0 1 0 1 0 0 ¥ ¥ ¥ ¥ 1 ¥ 8
¥ 2 1 ¥ 1 2 ¥
В
ариант
№ 7
1
.
0 0 1 1 0 0 2. ¥
3 4 9 ¥ ¥
¥ 3. ¥
4 3 5 6
1 0 0 0 0 1 12 ¥ ¥ 10 4 ¥ ¥ 4 ¥ 2 ¥ 1
1 0 0 0 1 0 ¥ ¥ ¥ 2 ¥ 1 ¥ 3 2 ¥ 1 1
0 1 0 0 0 1 ¥ ¥ ¥ ¥ 7 6 ¥ 5 ¥ 1 ¥ 3
0 0 1 0 1 0 ¥ ¥ ¥ ¥ ¥ ¥ 5 6 1 1 3 ¥
0 1 0 1 0 0 ¥ ¥ ¥ ¥ ¥ ¥ 8
¥ ¥ ¥ ¥ ¥ ¥ ¥
Вариант
№ 8
1
.
0 1 1 0 1 1 2. ¥
2 5 8 9 ¥ ¥
3. ¥ 1 3
4 5
1 0 1 1 0 1 ¥ ¥ ¥ 10 4 ¥ ¥ 1 ¥ 2 9 1
1 1 0 0 1 1 5 3 ¥ 2 1 ¥ ¥ 3 2 ¥ 1 1
0 1 0 0 0 1 ¥ ¥ ¥ ¥ 7 6 ¥ 4 9 1 ¥ 3
1 0 1 0 0 0 ¥ ¥ ¥ ¥ ¥ ¥ 5 5 1 1 3 ¥
1 1 1 1 0 0 ¥ ¥ ¥ ¥ ¥ ¥ 9
¥ ¥ ¥ ¥ ¥ ¥ ¥
В
ариант
№ 9
1 . 0 1 0 1 1 1 2. ¥ 2 5 14 ¥ ¥ ¥ 3. ¥ 5 3 10 7
1 0 0 1 0 0 11 ¥ ¥ 12 6 ¥ ¥ 5 ¥ 1 2 4
0 0 0 1 1 0 ¥ ¥ ¥ 3 ¥ 2 ¥ 3 1 ¥ 5 6
1 1 1 0 1 0 ¥ ¥ ¥ ¥ 9 8 ¥ 10 2 5 ¥ 3
1 0 1 1 0 1 ¥ ¥ ¥ ¥ ¥ ¥ 7 7 4 6 3 ¥
1 0 0 0 1 0 ¥ ¥ ¥ ¥ ¥ ¥ 10
¥ ¥ ¥ ¥ ¥ ¥ ¥
Вариант № 10
1
.
0 1 1 0 1 1 2. ¥
¥ 5 4 2 3 9
3. ¥ 7 2 11 7
1 0 0 1 1 1 ¥ ¥ 1 1 ¥ 1 6 7 ¥ 3 ¥ 4
1 0 0 0 1 0 4 ¥ ¥ 1 1 ¥ 3 2 3 ¥ 1 5
0 1 0 0 0 1 ¥ 2 1 ¥ 1 ¥ ¥ 11 ¥ 1 ¥ 3
1 1 1 0 0 1 ¥ ¥ 2 2 ¥ 1 6 7 4 5 3 ¥
1 1 0 1 1 0 1 5 ¥ 1 1 ¥ ¥
2 ¥ 1 ¥ 1 2 ¥
В
ариант
№ 11
1. 0 0 1 0 1 0 2. ¥ 4 9 ¥ 3 1 ¥ 3. ¥ 1 ¥ 4 5
0 0 0 1 0 1 3 ¥ 2 1 ¥ ¥ 4 1 ¥ 8 ¥ 7
1 0 0 0 1 0 1 1 ¥ ¥ 10 ¥ 1 ¥ 8 ¥ 10 1
0 1 0 0 0 1 ¥ 3 1 ¥ 1 ¥ ¥ 4 ¥ 10 ¥ 13
1 0 1 0 0 0 ¥ ¥ 2 ¥ ¥ 1 5 5 7 1 13 ¥
0 1 0 1 0 0 ¥ 3 ¥ 1 2 ¥ ¥
¥ ¥ 2 ¥ ¥ 2 ¥
Вариант
№ 12
1
.
0 0 1 0 1 0 2. ¥
¥ 9 ¥
10 2 12 3. ¥ 1
5 4 6
0 0 0 1 0 1 1 ¥ ¥ ¥ 1 2 4 1 ¥ 2 6 3
1 1 0 0 1 1 2 1 ¥ ¥ 1 ¥ 2 5 2 ¥ 1 7
0 0 0 0 0 0 ¥ 1 1 ¥ ¥ 1 15 4 6 1 ¥ 4
1 1 1 0 0 0 1 2 ¥ 2 ¥ ¥ ¥ 6 3 7 4 ¥
0 1 0 1 0 0 ¥ ¥ ¥ ¥ 1 ¥ 8
¥ 2 1 ¥ 1 2 ¥
В ариант № 13
1 . 0 0 0 0 0 0 2. ¥ 5 6 15 ¥ ¥ ¥ 3. ¥ 12 6 10 4
1 0 0 1 0 1 ¥ ¥ ¥ 13 7 ¥ ¥ 12 ¥ 2 5 6
1 0 0 0 1 0 ¥ ¥ ¥ 4 ¥ 3 ¥ 6 2 ¥ 10 12
1 1 1 0 0 0 ¥ ¥ ¥ ¥ 10 9 ¥ 10 5 10 ¥ 6
1 1 0 0 0 0 ¥ ¥ ¥ ¥ ¥ ¥ 8 4 6 12 6 ¥
0 1 0 0 1 0 ¥ ¥ ¥ ¥ ¥ ¥ 11
1 ¥ ¥ ¥ ¥ ¥ ¥
В
ариант
№ 14
1 . 0 0 1 1 0 0 2. ¥ 2 3 9 ¥ ¥ ¥ 3. ¥ 3 2 4 5
1 0 0 0 0 1 12 ¥ ¥ 10 4 ¥ ¥ 3 ¥ 2 ¥ 1
1 0 0 0 1 0 ¥ ¥ ¥ 2 ¥ 1 ¥ 2 2 ¥ 1 1
0 1 0 0 0 1 ¥ ¥ ¥ ¥ 7 6 ¥ 4 ¥ 1 ¥ 3
0 0 1 0 1 0 ¥ ¥ ¥ ¥ ¥ ¥ 5 5 1 1 3 ¥
0 1 0 1 0 0 ¥ ¥ ¥ ¥ ¥ ¥ 8
¥ ¥ ¥ ¥ ¥ ¥ ¥
В
ариант
№ 15
1 . 0 1 0 1 0 0 2. ¥ 2 5 10 ¥ ¥ ¥ 3. ¥ 6 3 10 4
1 0 0 1 0 0 ¥ ¥ ¥ 12 6 ¥ ¥ 6 ¥ 1 2 3
0 0 0 0 1 1 ¥ ¥ ¥ 3 ¥ 1 ¥ 3 1 ¥ 8 6
1 1 0 0 1 1 ¥ ¥ ¥ ¥ 9 8 ¥ 10 2 8 ¥ 3
0 0 1 1 0 0 ¥ ¥ ¥ ¥ ¥ ¥ 7 4 3 6 3 ¥
0 0 1 1 0 0 ¥ ¥ ¥ ¥ ¥ ¥ 10
¥ ¥ ¥ ¥ ¥ ¥ ¥
В
ариант
№ 16
1 . 0 0 0 0 1 1 2. ¥ ¥ 5 4 2 2 10 3. ¥ 4 2 10 6
0 0 1 1 0 0 ¥ ¥ 2 1 ¥ 2 1 4 ¥ 3 ¥ 4
0 1 0 0 1 0 2 ¥ ¥ 1 1 ¥ 3 2 3 ¥ 1 5
0 1 0 0 0 1 ¥ 2 1 ¥ 1 ¥ ¥ 10 ¥ 1 ¥ 3
1 0 1 0 0 0 ¥ ¥ 2 2 ¥ 1 6 6 4 5 3 ¥
1 0 0 1 0 0 1 5 ¥ 1 1 ¥ ¥
2 ¥ 1 ¥ 1 2 ¥
Вариант № 17
1 . 0 0 1 0 1 0 2. ¥ 4 9 8 3 1 ¥ 3. ¥ 2 ¥ 3 5
0 0 0 1 0 1 3 ¥ 2 1 ¥ ¥ 4 2 ¥ 8 ¥ 7
1 0 0 0 1 0 1 1 ¥ ¥ ¥ ¥ 1 ¥ 8 ¥ 10 1
0 1 0 0 0 1 ¥ 3 1 ¥ 1 ¥ ¥ 3 ¥ 10 ¥ 12
1 0 1 0 0 0 ¥ ¥ 2 ¥ ¥ 1 5 5 7 1 12 ¥
0 1 0 1 0 0 ¥ 3 ¥ 2 2 ¥ ¥
¥ ¥ 2 ¥ ¥ 2 ¥
Вариант № 18
1 . 0 0 1 0 1 0 2. ¥ ¥ 9 ¥ 10 2 12 3. ¥ 1 3 4 5
0 0 0 0 0 0 1 ¥ ¥ ¥ 1 2 4 1 ¥ 2 6 8
1 0 0 0 1 0 2 1 ¥ ¥ 1 ¥ 2 3 2 ¥ 1 7
0 1 0 0 0 1 ¥ 1 1 ¥ ¥ 1 ¥ 4 6 1 ¥ 4
1 0 1 0 0 0 1 2 9 2 ¥ ¥ ¥ 5 8 7 4 ¥
0 1 0 1 0 0 ¥ ¥ ¥ ¥ 1 ¥ 8
¥ 2 1 ¥ 1 2 ¥
Вариант
№ 19
1 . 0 1 1 0 1 1 2. ¥ 3 5 12 20 ¥ ¥ 3. ¥ 1 6 5 14
1 0 0 1 0 0 ¥ ¥ ¥ 13 8 ¥ ¥ 1 ¥ 3 4 6
1 0 0 1 1 1 ¥ ¥ ¥ 5 ¥ 3 ¥ 6 3 ¥ 10 12
0 1 1 0 1 1 ¥ ¥ ¥ ¥ 10 9 ¥ 5 4 10 ¥ 6
1 0 1 1 0 1 ¥ ¥ ¥ ¥ ¥ ¥ 8 14 6 12 6 ¥
1 0 1 1 1 0 ¥ ¥ ¥ ¥ ¥ ¥ 11
¥ ¥ ¥ ¥ ¥ ¥ ¥
Вариант № 20
1 . 0 1 0 0 1 0 2. ¥ 1 5 7 9 ¥ ¥ 3. ¥ 6 3 4 5
1 0 0 1 0 0 ¥ ¥ ¥ 10 4 ¥ ¥ 6 ¥ 2 9 1
1 0 0 0 1 1 5 3 ¥ ¥ 1 ¥ ¥ 3 2 ¥ 1 4
0 1 0 0 0 1 ¥ ¥ ¥ ¥ 7 6 ¥ 4 9 1 ¥ 3
0 0 1 0 0 0 ¥ ¥ ¥ ¥ ¥ ¥ 4 5 1 4 3 ¥
0 1 1 0 0 0 ¥ ¥ ¥ ¥ ¥ ¥ 9
¥ ¥ ¥ ¥ ¥ ¥ ¥
В ариант № 21
1 . 0 1 0 1 1 1 2. ¥ 1 5 15 ¥ ¥ ¥ 3. ¥ 5 3 6 7
1 0 0 1 0 0 ¥ ¥ 11 12 6 ¥ ¥ 5 ¥ 1 2 4
0 0 0 1 1 0 ¥ ¥ ¥ 3 ¥ 2 ¥ 3 1 ¥ 5 6
1 1 1 0 1 0 ¥ ¥ ¥ ¥ 9 8 ¥ 6 2 5 ¥ 3
1 0 1 1 0 1 ¥ ¥ ¥ ¥ ¥ ¥ 7 7 4 6 3 ¥
1 0 0 0 1 0 ¥ ¥ ¥ ¥ ¥ ¥ 10
¥ ¥ ¥ ¥ ¥ ¥ ¥
Вариант № 22
1 . 0 0 1 0 1 0 2. ¥ ¥ 3 4 1 5 9 3. ¥ 7 2 11 3
0 0 0 0 0 0 ¥ ¥ 1 2 ¥ 1 6 7 ¥ 3 ¥ 4
0 1 0 0 1 1 4 ¥ ¥ 2 1 ¥ 3 2 3 ¥ 1 5
0 1 0 0 0 1 ¥ 2 3 ¥ 1 ¥ ¥ 11 ¥ 1 ¥ 3
1 1 1 0 0 0 ¥ ¥ 2 2 ¥ 1 6 3 4 5 3 ¥
0 0 0 1 1 0 1 5 ¥ 1 1 ¥ ¥
2 ¥ 1 ¥ 1 2 ¥
В
ариант
№ 23
1 . 0 0 1 0 1 0 2. ¥ 4 9 ¥ 3 1 ¥ 3. ¥ 1 9 4 5
0 0 0 1 0 1 3 ¥ 2 1 ¥ ¥ 4 1 ¥ 8 ¥ 7
1 0 0 0 1 0 1 1 ¥ ¥ 10 14 1 9 8 ¥ 10 1
0 1 0 0 0 1 ¥ 3 1 ¥ 1 ¥ ¥ 4 ¥ 10 ¥ 13
1 0 1 0 0 0 ¥ ¥ 2 ¥ ¥ 1 5 5 7 1 13 ¥
0 1 0 1 0 0 ¥ 3 ¥ 1 2 ¥ ¥
¥ ¥ 2 ¥ ¥ 2 ¥
В
ариант
№ 24
1. 0 0 1 0 1 0 2. ¥ ¥ 8 ¥ 10 3 12 3. ¥ 3 2 4 6
0 0 0 1 0 0 1 ¥ ¥ ¥ 1 2 3 3 ¥ 5 6 3
0 1 0 0 1 0 2 1 ¥ ¥ 1 ¥ 2 2 5 ¥ 1 7
0 0 0 0 0 1 ¥ 1 1 ¥ ¥ 1 15 4 6 1 ¥ 4
0 1 1 0 0 0 1 2 ¥ 2 ¥ ¥ ¥ 6 3 7 4 ¥
0 1 0 0 0 0 ¥ ¥ ¥ ¥ 1 ¥ 8
¥ 2 1 ¥ 1 2 ¥
В
ариант
№ 25
1 . 0 0 1 0 0 1 2. ¥ ¥ 5 4 2 2 10 3. ¥ 1 2 8 5
0 0 1 1 1 1 ¥ ¥ 2 1 ¥ 2 1 1 ¥ 3 ¥ 4
1 1 0 0 0 0 2 ¥ ¥ 1 1 ¥ 3 2 3 ¥ 1 5
0 1 0 0 0 1 12 2 1 ¥ 1 ¥ ¥ 8 ¥ 1 ¥ 3
0 1 0 0 0 1 ¥ ¥ 2 2 ¥ 1 6 5 4 5 3 ¥
1 1 0 1 1 0 1 5 ¥ 1 1 ¥ ¥
2 ¥ 1 ¥ 1 2 ¥
Вариант
№ 26
1
.
0 0 0 0 1 0 2. ¥
4 9 8 3 2 ¥
3. ¥ 2 9 3 5
0 0 0 1 0 0 3 ¥ 2 1 ¥ ¥ 5 2 ¥ 8 ¥ 7
1 0 0 0 1 0 2 1 ¥ ¥ ¥ ¥ 1 9 8 ¥ 10 1
0 1 0 0 0 1 ¥ 3 1 ¥ 1 ¥ ¥ 3 ¥ 10 ¥ 12
0 0 0 0 0 0 ¥ ¥ 2 ¥ ¥ 1 5 5 7 1 12 ¥
0 1 0 0 0 0 ¥ 3 ¥ 2 2 ¥ ¥
¥ ¥ 2 ¥ ¥ 2 ¥
В
ариант
№ 27
1 . 0 0 1 0 1 0 2. ¥ ¥ 9 ¥ 8 1 12 3. ¥ 1 3 7 2
0 0 1 1 1 1 1 ¥ ¥ ¥ 2 2 4 1 ¥ 5 6 8
1 1 0 0 1 0 2 1 ¥ ¥ 1 ¥ 2 3 5 ¥ 1 7
0 1 0 0 0 1 ¥ 1 1 ¥ ¥ 1 ¥ 7 6 1 ¥ 4
1 1 1 0 0 0 1 2 9 2 ¥ ¥ ¥ 2 8 7 4 ¥
0 1 0 1 0 0 ¥ ¥ ¥ ¥ 1 ¥ 8
¥ 2 1 ¥ 1 2 ¥
В
ариант
№ 28
1 . 0 1 1 0 1 1 2. ¥ 3 5 12 20 ¥ ¥ 3. ¥ 1 6 5 14
1 0 0 1 0 0 ¥ ¥ ¥ 13 8 ¥ ¥ 1 ¥ 3 4 6
1 0 0 1 1 1 ¥ ¥ ¥ 5 ¥ 3 ¥ 6 3 ¥ 10 12
0 1 1 0 1 1 ¥ ¥ ¥ ¥ 10 9 ¥ 5 4 10 ¥ 6
1 0 1 1 0 1 ¥ ¥ ¥ ¥ ¥ ¥ 8 14 6 12 6 ¥
1 0 1 1 1 0 ¥ ¥ ¥ ¥ ¥ ¥ 11
¥ ¥ ¥ ¥ ¥ ¥ ¥
В ариант № 29
1. 0 1 0 0 1 0 2. ¥ 1 8 6 7 ¥ ¥ 3. ¥ 2 3 4 5
1 0 0 1 0 0 ¥ ¥ ¥ 10 4 ¥ ¥ 2 ¥ 6 9 1
1 0 0 0 1 1 5 3 ¥ ¥ 1 ¥ ¥ 3 6 ¥ 1 4
0 1 0 0 0 1 ¥ ¥ ¥ ¥ 7 6 ¥ 4 9 1 ¥ 3
0 0 1 0 0 0 ¥ ¥ ¥ ¥ ¥ ¥ 4 5 1 4 3 ¥
0 1 1 0 0 0 ¥ ¥ ¥ ¥ ¥ ¥ 9
¥ ¥ ¥ ¥ ¥ ¥ ¥
В ариант № 30
1. 0 1 0 1 1 1 2. ¥ 2 4 13 ¥ ¥ ¥ 3. ¥ 5 3 6 4
1 0 0 1 0 0 ¥ ¥ 11 12 6 ¥ ¥ 5 ¥ 1 2 7
0 0 0 1 1 0 ¥ ¥ ¥ 3 ¥ 2 ¥ 3 1 ¥ 5 6
1 1 1 0 1 0 ¥ ¥ ¥ ¥ 9 8 ¥ 6 2 5 ¥ 3
1 0 1 1 0 1 ¥ ¥ ¥ ¥ ¥ ¥ 7 4 7 6 3 ¥
1 0 0 0 1 0 ¥ ¥ ¥ ¥ ¥ ¥ 10
¥ ¥ ¥ ¥ ¥ ¥ ¥