| Graphs Discussed on TTL-Problem Page |
This page gives edge-lists for all the graphs described on this page. All of these were auto-generated in order to avoid errors in the edge lists and to verify the valencies and diameters.
— any K, D=1 —
Graph Name: K3
Nodes: 3
Edges: 3
Valency: 2
Diameter: 1
0 1
0 2
1 2
Graph Name: K4
Nodes: 4
Edges: 6
Valency: 3
Diameter: 1
0 1
0 2
0 3
1 2
1 3
2 3
Graph Name: K5
Nodes: 5
Edges: 10
Valency: 4
Diameter: 1
0 1
0 2
0 3
0 4
1 2
1 3
1 4
2 3
2 4
3 4
Graph Name: K6
Nodes: 6
Edges: 15
Valency: 5
Diameter: 1
0 1
0 2
0 3
0 4
0 5
1 2
1 3
1 4
1 5
2 3
2 4
2 5
3 4
3 5
4 5
— K=2, any D —
Graph Name: C3
Nodes: 3
Edges: 3
Valency: 2
Diameter: 1
0 1
1 2
2 0
Graph Name: C5
Nodes: 5
Edges: 5
Valency: 2
Diameter: 2
0 1
1 2
2 3
3 4
4 0
Graph Name: C7
Nodes: 7
Edges: 7
Valency: 2
Diameter: 3
0 1
1 2
2 3
3 4
4 5
5 6
6 0
— K=3, D=2 —
Graph Name: K3,3 = C6(1,3)
Nodes: 6
Edges: 9
Valency: 3
Diameter: 2
0 1
0 3
0 5
1 2
1 4
2 3
2 5
3 4
4 5
Graph Name: C8(1,4)
Nodes: 8
Edges: 12
Valency: 3
Diameter: 2
0 1
0 4
0 7
1 2
1 5
2 3
2 6
3 4
3 7
4 5
5 6
6 7
Graph Name: P
Nodes: 10
Edges: 15
Valency: 3
Diameter: 2
0 1
0 4
0 5
1 2
1 6
2 3
2 7
3 4
3 8
4 9
5 7
5 8
6 8
6 9
7 9
— K=3, D=3 —
Graph Name: C = Cml8(2:0,3)
Nodes: 8
Edges: 12
Valency: 3
Diameter: 3
0 1
0 3
0 7
1 2
1 6
2 3
2 5
3 4
4 5
4 7
5 6
6 7
Graph Name: C10(1,5)
Nodes: 10
Edges: 15
Valency: 3
Diameter: 3
0 1
0 5
0 9
1 2
1 6
2 3
2 7
3 4
3 8
4 5
4 9
5 6
6 7
7 8
8 9
Graph Name: C12(1,6)
Nodes: 12
Edges: 18
Valency: 3
Diameter: 3
0 1
0 11
0 6
1 2
1 7
2 3
2 8
3 4
3 9
4 10
4 5
5 11
5 6
6 7
7 8
8 9
9 10
10 11
Graph Name: PP7(1,3) K2
Nodes: 14
Edges: 21
Valency: 3
Diameter: 3
0 1
0 6
0 7
1 2
1 8
2 3
2 9
3 10
3 4
4 11
4 5
5 12
5 6
6 13
7 10
7 11
8 11
8 12
9 12
9 13
10 13
Graph Name: PP7(1,2) K2
Nodes: 14
Edges: 21
Valency: 3
Diameter: 3
0 1
0 6
0 7
1 2
1 8
2 3
2 9
3 10
3 4
4 11
4 5
5 12
5 6
6 13
7 12
7 9
8 10
8 13
9 11
10 12
11 13
Graph Name: Heawood
Nodes: 14
Edges: 21
Valency: 3
Diameter: 3
0 1
0 13
0 5
1 10
1 2
2 3
2 7
3 12
3 4
4 5
4 9
5 6
6 11
6 7
7 8
8 13
8 9
9 10
10 11
11 12
12 13
— K=4, D=2 —
Graph Name: O = C6(1,2)
Nodes: 6
Edges: 12
Valency: 4
Diameter: 2
0 1
0 2
0 4
0 5
1 2
1 3
1 5
2 3
2 4
3 4
3 5
4 5
Graph Name: K4,4 = C8(1,3)
Nodes: 8
Edges: 16
Valency: 4
Diameter: 2
0 1
0 3
0 5
0 7
1 2
1 4
1 6
2 3
2 5
2 7
3 4
3 6
4 5
4 7
5 6
6 7
Graph Name: K3 × K3
Nodes: 9
Edges: 18
Valency: 4
Diameter: 2
0 1
0 2
0 3
0 6
1 2
1 4
1 7
2 5
2 8
3 4
3 5
3 6
4 5
4 7
5 8
6 7
6 8
7 8
Graph Name: C11(1,3)
Nodes: 11
Edges: 22
Valency: 4
Diameter: 2
0 1
0 10
0 3
0 8
1 2
1 4
1 9
2 10
2 3
2 5
3 4
3 6
4 5
4 7
5 6
5 8
6 7
6 9
7 10
7 8
8 9
9 10
Graph Name: Cml15(5:1,4:2,5:3,7:4,4:4,7)
Nodes: 15
Edges: 30
Valency: 4
Diameter: 2
0 1
0 11
0 14
0 8
1 2
1 5
1 9
2 12
2 3
2 7
3 10
3 14
3 4
4 11
4 5
4 8
5 13
5 6
6 10
6 14
6 7
7 12
7 8
8 9
9 10
9 13
10 11
11 12
12 13
13 14
— K=3, D=4 —
Graph Name: C14(1,7)
Nodes: 14
Edges: 21
Valency: 3
Diameter: 4
0 1
0 13
0 7
1 2
1 8
2 3
2 9
3 10
3 4
4 11
4 5
5 12
5 6
6 13
6 7
7 8
8 9
9 10
10 11
11 12
12 13
Graph Name: C16(1,8)
Nodes: 16
Edges: 24
Valency: 3
Diameter: 4
0 1
0 15
0 8
1 2
1 9
2 10
2 3
3 11
3 4
4 12
4 5
5 13
5 6
6 14
6 7
7 15
7 8
8 9
9 10
10 11
11 12
12 13
13 14
14 15
Graph Name: PP11(1,3) K2
Nodes: 22
Edges: 33
Valency: 3
Diameter: 4
0 1
0 10
0 11
1 12
1 2
2 13
2 3
3 14
3 4
4 15
4 5
5 16
5 6
6 17
6 7
7 18
7 8
8 19
8 9
9 10
9 20
10 21
11 14
11 19
12 15
12 20
13 16
13 21
14 17
15 18
16 19
17 20
18 21
Graph Name: McGee = Cml24(3:1,12:2,7:0,17)
Nodes: 24
Edges: 36
Valency: 3
Diameter: 4
0 1
0 17
0 23
1 13
1 2
2 3
2 9
3 20
3 4
4 16
4 5
5 12
5 6
6 23
6 7
7 19
7 8
8 15
8 9
9 10
10 11
10 22
11 12
11 18
12 13
13 14
14 15
14 21
15 16
16 17
17 18
18 19
19 20
20 21
21 22
22 23
Graph Name: Tutte-Coxeter = Cml30(6:1,17:2,21:3,7)
Nodes: 30
Edges: 45
Valency: 3
Diameter: 4
0 1
0 13
0 29
1 18
1 2
2 23
2 3
3 10
3 4
4 27
4 5
5 14
5 6
6 19
6 7
7 24
7 8
8 29
8 9
9 10
9 16
10 11
11 12
11 20
12 13
12 25
13 14
14 15
15 16
15 22
16 17
17 18
17 26
18 19
19 20
20 21
21 22
21 28
22 23
23 24
24 25
25 26
26 27
27 28
28 29
— K=4, D=3 —
Graph Name: K2 × K3,3
Nodes: 12
Edges: 24
Valency: 4
Diameter: 3
0 1
0 10
0 2
0 6
1 11
1 3
1 7
2 3
2 4
2 8
3 5
3 9
4 10
4 5
4 6
5 11
5 7
6 7
6 8
7 9
8 10
8 9
9 11
10 11
Graph Name: K2 × P
Nodes: 20
Edges: 40
Valency: 4
Diameter: 3
0 1
0 10
0 2
0 8
1 11
1 3
1 9
2 12
2 3
2 4
3 13
3 5
4 14
4 5
4 6
5 15
5 7
6 16
6 7
6 8
7 17
7 9
8 18
8 9
9 19
10 11
10 14
10 16
11 15
11 17
12 13
12 16
12 18
13 17
13 19
14 15
14 18
15 19
16 17
18 19
Graph Name: Moebius D
Nodes: 20
Edges: 40
Valency: 4
Diameter: 3
0 10
0 16
0 19
0 4
1 11
1 19
1 2
1 3
2 12
2 18
2 6
3 13
3 4
3 5
4 14
4 8
5 15
5 6
5 7
6 10
6 16
7 17
7 8
7 9
8 12
8 18
9 10
9 11
9 19
10 14
11 12
11 13
12 16
13 14
13 15
14 18
15 16
15 17
17 18
17 19
Graph Name: PP7(1,2,3) K3
Nodes: 21
Edges: 42
Valency: 4
Diameter: 3
0 1
0 14
0 6
0 7
1 15
1 2
1 8
2 16
2 3
2 9
3 10
3 17
3 4
4 11
4 18
4 5
5 12
5 19
5 6
6 13
6 20
7 12
7 14
7 9
8 10
8 13
8 15
9 11
9 16
10 12
10 17
11 13
11 18
12 19
13 20
14 17
14 18
15 18
15 19
16 19
16 20
17 20
Graph Name: (4,6)-cage
Nodes: 26
Edges: 52
Valency: 4
Diameter: 3
0 1
0 17
0 25
0 5
1 10
1 2
1 22
2 19
2 3
2 7
3 12
3 24
3 4
4 21
4 5
4 9
5 14
5 6
6 11
6 23
6 7
7 16
7 8
8 13
8 25
8 9
9 10
9 18
10 11
10 15
11 12
11 20
12 13
12 17
13 14
13 22
14 15
14 19
15 16
15 24
16 17
16 21
17 18
18 19
18 23
19 20
20 21
20 25
21 22
22 23
23 24
24 25
Graph Name: PP7(1,2,3,2) C4
Nodes: 28
Edges: 56
Valency: 4
Diameter: 3
0 1
0 21
0 6
0 7
1 2
1 22
1 8
2 23
2 3
2 9
3 10
3 24
3 4
4 11
4 25
4 5
5 12
5 26
5 6
6 13
6 27
7 12
7 14
7 9
8 10
8 13
8 15
9 11
9 16
10 12
10 17
11 13
11 18
12 19
13 20
14 17
14 18
14 21
15 18
15 19
15 22
16 19
16 20
16 23
17 20
17 24
18 25
19 26
20 27
21 23
21 26
22 24
22 27
23 25
24 26
25 27
— K=5, D=2 —
Graph Name: PP9(1,3) K2 U PP9(2,4) K2
Nodes: 18
Edges: 45
Valency: 5
Diameter: 2
0 1
0 2
0 7
0 8
0 9
1 10
1 2
1 3
1 8
2 11
2 3
2 4
3 12
3 4
3 5
4 13
4 5
4 6
5 14
5 6
5 7
6 15
6 7
6 8
7 16
7 8
8 17
9 12
9 13
9 14
9 15
10 13
10 14
10 15
10 16
11 14
11 15
11 16
11 17
12 15
12 16
12 17
13 16
13 17
14 17
— K=3, D=5 —
Graph Name: D
Nodes: 20
Edges: 30
Valency: 3
Diameter: 5
0 16
0 19
0 4
1 19
1 2
1 3
2 18
2 6
3 4
3 5
4 8
5 6
5 7
6 10
7 8
7 9
8 12
9 10
9 11
10 14
11 12
11 13
12 16
13 14
13 15
14 18
15 16
15 17
17 18
17 19
— K=4, D=4 —
Graph Name: C × K2
Nodes: 16
Edges: 32
Valency: 4
Diameter: 4
0 1
0 3
0 7
0 8
1 2
1 6
1 9
2 10
2 3
2 5
3 11
3 4
4 12
4 5
4 7
5 13
5 6
6 14
6 7
7 15
8 11
8 15
8 9
9 10
9 14
10 11
10 13
11 12
12 13
12 15
13 14
14 15
Graph Name: C5 × C5
Nodes: 25
Edges: 50
Valency: 4
Diameter: 4
0 1
0 20
0 4
0 5
1 2
1 21
1 6
2 22
2 3
2 7
3 23
3 4
3 8
4 24
4 9
5 10
5 6
5 9
6 11
6 7
7 12
7 8
8 13
8 9
9 14
10 11
10 14
10 15
11 12
11 16
12 13
12 17
13 14
13 18
14 19
15 16
15 19
15 20
16 17
16 21
17 18
17 22
18 19
18 23
19 24
20 21
20 24
21 22
22 23
23 24
Graph Name: PP7(1,3) K2 × K2
Nodes: 28
Edges: 56
Valency: 4
Diameter: 4
0 1
0 14
0 6
0 7
1 15
1 2
1 8
2 16
2 3
2 9
3 10
3 17
3 4
4 11
4 18
4 5
5 12
5 19
5 6
6 13
6 20
7 10
7 11
7 21
8 11
8 12
8 22
9 12
9 13
9 23
10 13
10 24
11 25
12 26
13 27
14 15
14 20
14 21
15 16
15 22
16 17
16 23
17 18
17 24
18 19
18 25
19 20
19 26
20 27
21 24
21 25
22 25
22 26
23 26
23 27
24 27
Graph Name: Heawood × K2
Nodes: 28
Edges: 56
Valency: 4
Diameter: 4
0 1
0 13
0 14
0 5
1 10
1 15
1 2
2 16
2 3
2 7
3 12
3 17
3 4
4 18
4 5
4 9
5 19
5 6
6 11
6 20
6 7
7 21
7 8
8 13
8 22
8 9
9 10
9 23
10 11
10 24
11 12
11 25
12 13
12 26
13 27
14 15
14 19
14 27
15 16
15 24
16 17
16 21
17 18
17 26
18 19
18 23
19 20
20 21
20 25
21 22
22 23
22 27
23 24
24 25
25 26
26 27
Graph Name: PP9(1,2,3,4) C4
Nodes: 36
Edges: 72
Valency: 4
Diameter: 4
0 1
0 27
0 8
0 9
1 10
1 2
1 28
2 11
2 29
2 3
3 12
3 30
3 4
4 13
4 31
4 5
5 14
5 32
5 6
6 15
6 33
6 7
7 16
7 34
7 8
8 17
8 35
9 11
9 16
9 18
10 12
10 17
10 19
11 13
11 20
12 14
12 21
13 15
13 22
14 16
14 23
15 17
15 24
16 25
17 26
18 21
18 24
18 27
19 22
19 25
19 28
20 23
20 26
20 29
21 24
21 30
22 25
22 31
23 26
23 32
24 33
25 34
26 35
27 31
27 32
28 32
28 33
29 33
29 34
30 34
30 35
31 35
Graph Name: PP9(1,2,3,4,2) C5
Nodes: 45
Edges: 90
Valency: 4
Diameter: 4
0 1
0 36
0 8
0 9
1 10
1 2
1 37
2 11
2 3
2 38
3 12
3 39
3 4
4 13
4 40
4 5
5 14
5 41
5 6
6 15
6 42
6 7
7 16
7 43
7 8
8 17
8 44
9 11
9 16
9 18
10 12
10 17
10 19
11 13
11 20
12 14
12 21
13 15
13 22
14 16
14 23
15 17
15 24
16 25
17 26
18 21
18 24
18 27
19 22
19 25
19 28
20 23
20 26
20 29
21 24
21 30
22 25
22 31
23 26
23 32
24 33
25 34
26 35
27 31
27 32
27 36
28 32
28 33
28 37
29 33
29 34
29 38
30 34
30 35
30 39
31 35
31 40
32 41
33 42
34 43
35 44
36 38
36 43
37 39
37 44
38 40
39 41
40 42
41 43
42 44
Graph Name: PP11(1,2,4,3,5) C5
Nodes: 55
Edges: 110
Valency: 4
Diameter: 4
0 1
0 10
0 11
0 44
1 12
1 2
1 45
2 13
2 3
2 46
3 14
3 4
3 47
4 15
4 48
4 5
5 16
5 49
5 6
6 17
6 50
6 7
7 18
7 51
7 8
8 19
8 52
8 9
9 10
9 20
9 53
10 21
10 54
11 13
11 20
11 22
12 14
12 21
12 23
13 15
13 24
14 16
14 25
15 17
15 26
16 18
16 27
17 19
17 28
18 20
18 29
19 21
19 30
20 31
21 32
22 26
22 29
22 33
23 27
23 30
23 34
24 28
24 31
24 35
25 29
25 32
25 36
26 30
26 37
27 31
27 38
28 32
28 39
29 40
30 41
31 42
32 43
33 36
33 41
33 44
34 37
34 42
34 45
35 38
35 43
35 46
36 39
36 47
37 40
37 48
38 41
38 49
39 42
39 50
40 43
40 51
41 52
42 53
43 54
44 49
44 50
45 50
45 51
46 51
46 52
47 52
47 53
48 53
48 54
49 54
Graph Name: PP13(1,5,4,2,3,6) C6
Nodes: 78
Edges: 156
Valency: 4
Diameter: 4
0 1
0 12
0 13
0 65
1 14
1 2
1 66
2 15
2 3
2 67
3 16
3 4
3 68
4 17
4 5
4 69
5 18
5 6
5 70
6 19
6 7
6 71
7 20
7 72
7 8
8 21
8 73
8 9
9 10
9 22
9 74
10 11
10 23
10 75
11 12
11 24
11 76
12 25
12 77
13 18
13 21
13 26
14 19
14 22
14 27
15 20
15 23
15 28
16 21
16 24
16 29
17 22
17 25
17 30
18 23
18 31
19 24
19 32
20 25
20 33
21 34
22 35
23 36
24 37
25 38
26 30
26 35
26 39
27 31
27 36
27 40
28 32
28 37
28 41
29 33
29 38
29 42
30 34
30 43
31 35
31 44
32 36
32 45
33 37
33 46
34 38
34 47
35 48
36 49
37 50
38 51
39 41
39 50
39 52
40 42
40 51
40 53
41 43
41 54
42 44
42 55
43 45
43 56
44 46
44 57
45 47
45 58
46 48
46 59
47 49
47 60
48 50
48 61
49 51
49 62
50 63
51 64
52 55
52 62
52 65
53 56
53 63
53 66
54 57
54 64
54 67
55 58
55 68
56 59
56 69
57 60
57 70
58 61
58 71
59 62
59 72
60 63
60 73
61 64
61 74
62 75
63 76
64 77
65 71
65 72
66 72
66 73
67 73
67 74
68 74
68 75
69 75
69 76
70 76
70 77
71 77
— K=5, D=3 —
Graph Name: Robertson-Wegner
Nodes: 30
Edges: 75
Valency: 5
Diameter: 3
0 10
0 15
0 19
0 2
0 29
1 12
1 2
1 21
1 28
1 4
2 26
2 3
2 8
3 13
3 18
3 22
3 5
4 15
4 24
4 5
4 7
5 11
5 29
5 6
6 16
6 21
6 25
6 8
7 10
7 18
7 27
7 8
8 14
8 9
9 11
9 19
9 24
9 28
10 11
10 13
10 21
11 12
11 17
12 14
12 22
12 27
13 14
13 16
13 24
14 15
14 20
15 17
15 25
16 17
16 19
16 27
17 18
17 23
18 20
18 28
19 20
19 22
20 21
20 26
21 23
22 23
22 25
23 24
23 29
24 26
25 26
25 28
26 27
27 29
28 29
Graph Name: PP9(1,2,3,4) K4
Nodes: 36
Edges: 90
Valency: 5
Diameter: 3
0 1
0 18
0 27
0 8
0 9
1 10
1 19
1 2
1 28
2 11
2 20
2 29
2 3
3 12
3 21
3 30
3 4
4 13
4 22
4 31
4 5
5 14
5 23
5 32
5 6
6 15
6 24
6 33
6 7
7 16
7 25
7 34
7 8
8 17
8 26
8 35
9 11
9 16
9 18
9 27
10 12
10 17
10 19
10 28
11 13
11 20
11 29
12 14
12 21
12 30
13 15
13 22
13 31
14 16
14 23
14 32
15 17
15 24
15 33
16 25
16 34
17 26
17 35
18 21
18 24
18 27
19 22
19 25
19 28
20 23
20 26
20 29
21 24
21 30
22 25
22 31
23 26
23 32
24 33
25 34
26 35
27 31
27 32
28 32
28 33
29 33
29 34
30 34
30 35
31 35
— K=5, D=4 —
Graph Name: PP7(1,2,3,2) C4 × K2
Nodes: 56
Edges: 140
Valency: 5
Diameter: 4
0 1
0 21
0 28
0 6
0 7
1 2
1 22
1 29
1 8
2 23
2 3
2 30
2 9
3 10
3 24
3 31
3 4
4 11
4 25
4 32
4 5
5 12
5 26
5 33
5 6
6 13
6 27
6 34
7 12
7 14
7 35
7 9
8 10
8 13
8 15
8 36
9 11
9 16
9 37
10 12
10 17
10 38
11 13
11 18
11 39
12 19
12 40
13 20
13 41
14 17
14 18
14 21
14 42
15 18
15 19
15 22
15 43
16 19
16 20
16 23
16 44
17 20
17 24
17 45
18 25
18 46
19 26
19 47
20 27
20 48
21 23
21 26
21 49
22 24
22 27
22 50
23 25
23 51
24 26
24 52
25 27
25 53
26 54
27 55
28 29
28 34
28 35
28 49
29 30
29 36
29 50
30 31
30 37
30 51
31 32
31 38
31 52
32 33
32 39
32 53
33 34
33 40
33 54
34 41
34 55
35 37
35 40
35 42
36 38
36 41
36 43
37 39
37 44
38 40
38 45
39 41
39 46
40 47
41 48
42 45
42 46
42 49
43 46
43 47
43 50
44 47
44 48
44 51
45 48
45 52
46 53
47 54
48 55
49 51
49 54
50 52
50 55
51 53
52 54
53 55