Файл: Ху, Т. Целочисленное программирование и потоки в сетях.pdf
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ГРАНИ, ВЕРШИНЫ И МАТРИЦЫ |
475 |
° (С4. 2. (О, 1))
Грани
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'с т р о к а "''''\ 7 i,o |
7г,о |
7з, о 7о, 1 |
7 i,i |
72,1 |
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7з, 1 |
7о |
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Вершины |
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1 . (*0. l) |
*1, l) |
= ( 1 ) |
8- ( h , o> h , l) |
= ( 2 , 1 ) |
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2 . |
(*1, 0. |
= |
(3 ,1) |
0- |
(fi, |
i, |
h , |
l) |
= |
(2 , |
1) |
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3. |
(*1, о. h , |
о> G, i) = |
( 1 , 1 , 1 ) |
10 - |
(<i, |
o, |
h , |
l) |
= |
(1 , |
1) |
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4. |
(*3, O' |
*1, l) |
= (1 , 1) |
1 1 * |
( h , |
o> h , |
о, h , l) = |
( 1 ,1 > |
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5. |
(*1. O' |
*1, l) |
= |
(1 ,3) |
12. (#з, O' *3, 1) |
= |
(3 ,1 ) |
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6. |
(<i, O' |
h , |
i ) |
= (2, 1 ) |
13. |
(l2> lt |
<3, i) |
= ( 1 , |
2) |
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7. |
( h i o> |
h , |
l) |
= |
(1 , 1) |
14. |
(*3,0, |
h , |
i) |
= |
(1 .3 ) |
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Матрица инциденций Р (G4l 2, |
(О, 1)) |
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Грань |
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2 3 4 |
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6 7 8 |
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Р ( 0 2> 2, 2. ( 0, 0, 0)) |
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Грани |
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Строка |
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7i, 0, 0 7o,i,o 7 i,i, o 7o,o,i |
7 i,o ,i |
7 o ,i,i |
7 i,i,i |
7o |
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Вершины |
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1 - |
(*i, о,о) = |
(2) |
5. |
( h , |
0, i) = |
(2) |
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2 - |
(го, i,o ) = (2) |
6. ( h , |
1, i) = |
(2) |
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3- |
(*i, 1. о) = |
(2) |
7. |
(< i,i,i) = |
(2) |
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4. (<о, о, i) = (2)
ГРА Н И , В Е РШ И Н Ы И М А ТРИЦЫ |
477 |
P(G9, (0))
Грани
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Строка^^^^^ |
7i |
72 7з 74 75 7б 77 78 |
7о |
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И |
7 12 |
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И |
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8 10 |
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10 И 12 |
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7 14 |
12 10 |
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7 И |
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Вершины Р (G9, (0)) |
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1. |
(<i) |
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= |
(9) |
19. |
(*4, h ) |
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= |
(3,1) |
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2. |
(*i. h ) |
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= |
(1,4) |
20. |
( h ) |
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= |
(3) |
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3. |
( h ) |
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= |
(9) |
21. |
( h i |
h ) |
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= |
(2,1) |
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4. |
(**, h ) |
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= |
(3,1) |
22. |
(t-2i h ) |
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= |
(1,1) |
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5. |
( h ) |
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= |
(3) |
23. |
(t 5> h ) |
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= |
(4 ,1) |
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6. |
( h i |
h , |
h ) |
= |
(1,1,1) |
24. |
( h i |
h i |
h ) |
= |
(1,1,1) |
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7. |
( h , h ) |
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= |
(1,2) |
25. |
( t n |
h ) |
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= |
d ,2 ) |
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8. |
( h i |
h ) |
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= |
(1,4) |
26. |
( h i |
h ) |
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= |
(1,3) |
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9. |
( h ) |
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= |
(9) |
27. |
( h ) |
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= |
(9) |
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10. |
( h i |
h ) |
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= |
(4,1) |
28. |
( h i |
<s) |
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= |
(1,1) |
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11. |
( h i |
h ) |
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= |
(2 ,1) |
29. |
(<5, *e) |
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= |
(2,1) |
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12. |
( h i |
h i |
h ) |
= |
(1,1,1) |
30. |
( h i |
*6, h ) |
= |
(1,1,1) |
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13. |
( h , h ) |
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= |
(1,1) |
31. |
( h i |
h i |
(8)>= |
(1,1,1) |
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14. |
( h i |
<5) |
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= |
(1,3) |
32. |
( h i |
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= |
(4,1) |
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15. |
( h ) |
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= |
(9) |
33. |
( h i |
h ) |
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= |
(1,2) |
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16. |
(*i> *e) |
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= |
(3,1) |
34. |
( h i |
h ) |
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= |
(1,3) |
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17. |
(t i, |
h i |
h ) |
= |
(1,1,1) |
35. |
(t^i |
t$) |
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= |
(1,4) |
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18. |
( h , |
h ) |
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= |
(1,1) |
36. |
( h ) |
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= |
(9) |
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ПРИЛОЖЕНИЕ D
[ца ;енций P(G9, (0))
[ИНс |
1 |
2 |
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7 |
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12 |
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1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
2 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
1 |
1 |
3 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
1 |
1 |
1 |
1 |
1 |
1 |
4 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
1 |
0 |
1 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
1 |
1 |
1 |
1 |
1 |
5 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
1 |
1 |
0 |
1 |
0 |
0 |
1 |
1 |
0 |
1 |
1 |
1 |
1 |
1 |
6 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
0 |
0 |
1 |
0 |
1 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
7 |
0 |
0 |
1 |
1 |
0 |
1 |
1 |
0 |
0 |
1 |
0 |
0 |
1 |
0 |
0 |
1 |
0 |
1 |
1 |
0 |
1 |
1 |
1 |
1 |
8 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
1 |
0 |
1 |
1 |
1 |
1 |
9 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
0 |
1 |
1 |
1 |
1 |
10 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
0 |
1 |
1 |
1 |
И |
1 |
1 |
0 |
0 |
0 |
0 |
1 |
0 |
1 |
1 |
0 |
1 |
0 |
1 |
0 |
0 |
1 |
0 |
1 |
1 |
0 |
1 |
1 |
1 |
12 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
1 |
0 |
1 |
0 |
1 |
1 |
1 |
13 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
0 |
0 |
1 |
1 |
1 |
14 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
1 |
1 |
0 |
1 |
0 |
1 |
1 |
1 |
15 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
0 |
1 |
1 |
1 |
16 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
1 |
1 |
1 |
1 |
0 |
1 |
1 |
17 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
1 |
1 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
1 |
1 |
1 |
0 |
1 |
1 |
18 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
0 |
1 |
1 |
0 |
1 |
1 |
19 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
1 |
1 |
1 |
0 |
1 |
0 |
1 |
1 |
20 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
0 |
0 |
1 |
0 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
0 |
1 |
1 |
21 |
0 |
0 |
1 |
1 |
0 |
0 |
0 |
1 |
1 |
1 |
0 |
0 |
0 |
0 |
1 |
1 |
0 |
1 |
1 |
1 |
1 |
1 |
0 |
1 |
22 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
0 |
1 |
1 |
1 |
1 |
0 |
1 |
23 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
0 |
1 |
0 |
1 |
24 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
1 |
1 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
1 |
1 |
1 |
1 |
0 |
0 |
0 |
1 |
25 |
0 |
0 |
1 |
1 |
1 |
1 |
0 |
1 |
0 |
0 |
0 |
0 |
1 |
0 |
1 |
0 |
1 |
1 |
1 |
0 |
1 |
1 |
0 |
1 |
26 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
1 |
1 |
1 |
1 |
1 |
0 |
0 |
1 |
27 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
1 |
1 |
0 |
1 |
28 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
0 |
1 |
1 |
1 |
1 |
1 |
1 |
0 |
29 |
1 |
1 |
0 |
0 |
1 |
0 |
0 |
1 |
1 |
0 |
1 |
0 |
0 |
1 |
0 |
0 |
1 |
1 |
1 |
1 |
0 |
1 |
1 |
0 |
30 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
1 |
1 |
1 |
0 |
1 |
0 |
1 |
0 |
31 |
0 |
0 |
0 |
0 |
1 |
1 |
0 |
1 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
0 |
1 |
1 |
1 |
0 |
О |
32 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
1 |
1 |
0 |
О |
33 |
1 |
1 |
0 |
0 |
1 |
1 |
1 |
0 |
0 |
0 |
1 |
1 |
0 |
0 |
0 |
0 |
1 |
0 |
1 |
1 |
1 |
1 |
1 |
0 |
34 |
0 |
0 |
0 |
0 |
1 |
1 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
0 |
1 |
1 |
1 |
1 |
0 |
35 |
0 |
0 |
0 |
0 |
1 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
0 |
1 |
1 |
1 |
0 |
36 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
0 |
ГРАНИ, ВЕРШ ИНЫ И МАТРИЦЫ |
479 |
Р (G„, (6))
Грани
Вершины |
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1. |
(h) |
= (6) |
9. |
(f5) |
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= |
(3) |
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2. |
(h) |
= |
(3) |
10. |
(t6) |
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= |
d) |
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3. |
(h) |
= |
(2) |
11. |
(t4, i7) = |
(2,1) |
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4. |
( G ,y = (2,l) |
12. |
(t!,*7) = |
(1,2) |
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5. |
(t2. t4) = |
( l.l) |
13. |
(f3, t7) = |
(l,3) |
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6. |
(«з.<4) = |
(1.3) |
14. |
(i7) |
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= |
(6) |
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7. |
(«4) |
= |
(6) |
15. |
(f7, i 8) = |
( l,l) |
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8. |
(G,<5) = |
(1,1) |
16. |
((g) |
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= |
(3) |
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Матрица инциденций Р (Gg, |
(6)) |
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Грань |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 11 12 13 |
14 |
15 |
16 |
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Вершин |
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1 |
0 |
0 |
1 |
0 |
0 |
0 |
1 |
0 |
0 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
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2 |
0 |
1 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
1 |
1 |
1 |
1 |
1 |
|
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|
3 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
0 |
1 |
1 |
1 |
1 |
1 |
|
|
|
4 |
0 |
0 |
1 |
1 |
0 |
1 |
1 |
0 |
0 |
1 |
1 |
0 |
1 |
1 |
1 |
1 |
|
|
|
5 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
0 |
1 |
0 |
1 |
1 |
1 |
1 |
|
|
|
6 |
1 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
1 |
1 |
0 |
0 |
1 |
1 |
1 |
1 |
|
|
|
7 |
1 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
1 |
1 |
1 |
0 |
1 |
1 |
1 |
1 |
|
|
|
8 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
0 |
1 |
1 |
1 |
0 |
1 |
1 |
1 |
|
|
|
9 |
1 |
1 |
0 |
0 |
1 |
0 |
0 |
1 |
1 |
1 |
1 |
1 |
0 |
1 |
1 |
1 |
|
|
|
10 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
0 |
1 |
1 |
|
|
|
11 |
1 |
0 |
0 |
1 |
0 |
1 |
0 |
1 |
1 |
1 |
1 |
0 |
1 |
1 |
0 |
1 |
|
|
|
12 |
0 |
0 |
0 |
1 |
1 |
0 |
1 |
1 |
0 |
1 |
1 |
1 |
1 |
1 |
0 |
1 |
|
|
|
13 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
1 |
1 |
1 |
0 |
1 |
1 |
1 |
0 |
1 |
|
|
|
14 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
0 |
1 |
|
|
|
15 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
0 |
0 |
|
|
|
16 |
1 |
1 |
1 |
0 |
0 |
1 |
0 |
0 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
0 |