j () i, () i j. K () - ( ), K , K , - ( , K ). , , , - ( ) , ( ), - . , () - ( ). () - , ( ).
20. , .19 ( .7-f). - : { A, B, C, D }, { E, F, G, H, I, J }, { R }■
21. , .20 ( .10-6). 1 3 ( a b), . 2 4 , 3 4, 4 2. , : {1, 3}, {2} {4}■
10. .7 ■
11. .10 ■
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.19 | .20 |
22. , .21a ( .5-12), - . ( ) , .21b, , , .
.21a | .21b |
23. , .20, , c d . , .22. , , : {1, 3}, {2} {4}. , a b , c d ■
.22
12. .5, 7 .10, - / () . - () á V, E ñ (á V, ñ), 4 6 ■
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24. 23 , 300 1200 . . , , , , ■
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, , - . , i - i. i - , , -
.23
i. , , . .
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25. , .6, :
áá2, 4, 5ñ, á3, 4, 5ñ, á2, 4ñ, á2, 3, 5ñ, á1, 2, 4ññ■
26. , .24 ( .19 - ), :áá2, 3, 4ñ, á1, 3ñ, á1, 2, 4ñ, á1, 3ñ, á6, 8, 9ñ, á5, 7, 10ñá6, 8ñ, á5, 7ñ, á5ñ, á6ñ, áññ. (11-) : 11 , ■
27. , .25 ( .10-5), : áá3, 4ñ, á1, 4ñ, á2, 4ñ, áññ. 4- , 4 .
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13. , 12, - (. 25 27) ■
.24 | .25 |
. , . . - M n ( n ). i - M [ i ] = . ( , ). -1.
-1 +1. x -1 ( ) , , -1. , , , x -1 +1. -1 , +1 1- . - , . y, -2 1 2. , , -3, ., , . i - i - .
28. 26 (.24). : áá2, 3, 4ñ, á1, 3ñ, á1, 2, 4ñ, á1, 3ñ, á6, 8, 9ñ, á5, 7, 10ñá6, 8ñ, á5, 7ñ, á5ñ, á6ñ, áññ.
1. . 11. M 11 M [1] = -1.
2. M [2] = -1, M [3] = -1, M [4] = -1.
3. 1 2, 3, 4,
M [1] = 1.
4. 2 -1. 1, 3 -. M [2] = 1.
5. 3 -1. 1, 2, 4 -. M [3] = 1.
6. 4 -1. 1, 3 -. M [4] = 1.
7. -1 (M [1] = M [2] = M [3] = M [4] = 1), 5 M [5] = -2.
8. 5 6, 8, 9 M [6] = -2, M [8] = -2, M [9] = -2.
9. 5 6, 8, 9,
M [5] = 2.
10. 6 -2. 5 ( ), 7 10 ( ). M [7] = -2, M [10] = -2.
11. M [6] = 2.
12. 7 -2. 6 8 ( ). M [7] = 2.
13. 8 -2. 5 ( ). M [8] = 2.
14. 9 -2. 5 ( ). M [9] = 2.
15. 10 -2. 6 ( ). M [10] = 2.
16. -2 (M [5] = M [6] = M [7] = M [8] = M [9] = M [10] = 2), 11 M [11] = -3.
17. , 11. , 11, , M [11]: M [11] = 3.
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18. -3 , . , .
M: M = á1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3ñ. , 1- 1, 2, 3, 4; 2- 5, 6, 7, 8, 9, 10; 3- 11■
14. , 13, (. 28) ■
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5.1. ʸ . - , . ʸ - - XVIII- -.
.26. (1707 1783) | .27. XVIII |
(Leonhard Euler) 15 1707 . , , - . , . - . , , .
. -. , - . . ʸ, -, . - , , , (.27). :
1. Kramer-Brucke ( )
2. GruneBrucke( )
3. Kottel-Brucke( )
4. Schmiede-Brucke( )
5. Holz-Brucke( )
6. Hohe-Brucke( )
7. Honig-Brucke( )
1736 , : , . .28 ʸ- (, ).
, .28. - , , . , .3. ,
.28
(. 2). , - . (. 4) : .3 , ? , 4. - .
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5.2. . : , . 1873 150 . . , .
29. , .29 a. , , .
.29
{3, 5} ; , . 29 b. {7, 8} ; , - .29 c; 8 . {6, 7} , .29 d; ( {3, 5} {7, 8}).
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1. . . - .
2. . , : , . . .
3. 2 , .
30. , .30 a. , . , .
.30
3. 3 2, 5. - 5, {3, 5} ( 30 b ). , {3, 5}. - 4, 6 7. {5, 4}, {5, 6} {5, 7} {3, 5} , 2- . {5, 7}. .30 b 2, : 3→5→7.
, 7 1, 4 6. {7, 1} , {3, 5} {5, 7} (. .30 b). ({7, 4} {7, 6}), . {7, 6 }, {7,6} 3→5→7→6; .30 b. , - {7, 1} , .30 b, - - {7, 4} {7, 6}. 2 - .
, {3, 5}, {5, 7} {7,6} .30 . 6 .30 {6,5}, . , {6,5}, , {6,5} , . - (. .30 ). 3→5→7→6→5→4→7→
1→2→3. 9 . - .30 d.
15. , .31, , . , 30. -, , , - ■
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- . -. , (), (-: ). , . , , . , , . ( ) .
31. .32. X = {{1,7}, {3,11}, {5,10}}, , . Y = {{4,7}, {1,8}, {3,9}, {5,10}, {6,11}}, , . , - 5 , , 5 , - , -, ■
.31
.32.
1. (. 1, 3 5).
1. G = á V, E, F ñ, V = {1, 2, 3, 4}, E ={ a, b, c, d, e, f, g, h }, F (a) = F (b) = {1, 3}, F (c) = F (d) = {2, 4}, F (e) = {2, 3}, F (f) = {1, 4}, F (g) = {3, 4}, F (h) = {1, 2}.
2. G = á V, E ñ, V = {1, 2, 3, 4}, E = {{1, 2}, {2, 3}, {3, 4}, {1, 4}, {2, 4}}.
3. G = á V, E, F ñ, V = {1, 2, 3}, E ={ a, b, c, d, e, f }, F (a) = F (b) = {1, 2}, F (c) = F (d) = {1, 3}, F (e) = F (f) = {2, 3}.
4. G = á V, E, F ñ, V = {1, 2, 3}, E ={ a, b, c, d, e }, F (a) = F (b) = {1, 2}, F (c) = F (d) = {1, 3}, F (e) = {2, 3}.
5. G = á V, E ñ, V = {1, 2, 3, 4}, E = {{1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}}.
6. G = á V, E ñ, V = {1, 2, 3, 4, 5, 6}, E = {{2}, {6}, {1, 4}, {1, 5}, {1, 6}, {2, 5}, {3, 6}}.
7. G = á V, E, F ñ, V = {1, 2, 3, 4}, E ={ a, b, c }, F (a) = F (b) = {1, 2}, F (c) = {3, 4}.
8. G = á V, E ñ, V = {1, 2, 3, 4, 5, 6, 7}, E = {{7}, {1, 2}, {2, 3}, {3, 4}, {5, 6}, {1, 6}}.
9. G = á V, E ñ, V = {1, 2, 3, 4, 5}, E = {{5}, {1, 2}, {2, 3}, {3, 4}, {4, 5}, {1, 5}}.
10. G = á V, E, F ñ, V = {1, 2, 3}, E ={ a, b, c, d, e }, F (a) = F (b) = {1, 2}, F (c) = {1, 3}, F (d) = {2, 3}, F (e) = {3}.
11. G = á V, E, F ñ, V = {1, 2}, E ={ a, b, c }, F (a) = F (b) = F (c) = {1, 2}.
12. G = á V, E ñ, V = {1, 2, 3, 4}, E = {{1, 2}, {2, 3}, {3, 4}, {1, 4}, {2, 4}, {1, 3}}.
13. G = á V, E ñ, V = {1, 2, 3, 4, 5, 6}, E = {{1, 4}, {1, 5}, {1, 6}, {2, 4}, {2, 5}, {2, 6}, {3, 4}, {3, 5}, {3, 6}}.
14. G = á V, E, F ñ, V = {1, 2, 3, 4}, E ={ a, b, c, d }, F (a) = F (b) = {1, 3}, F (c) = {1, 4}, F (d) = {2, 3}.
15. G = á V, E, F ñ, V = {1, 2, 3, 4}, E ={ a, b, c, d, e }, F (a) = {1, 4}, F (b) = {1, 2}, F (c) = {3, 4}, F (d) = F (e) = {2, 3} ■
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2. , 1, á V, E ñ á V, E, F ñ (. 1, 3 5)■
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