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On this page are computer-accessible forms for the graph C4[ 136, 9 ] = MPS(4,68;13).

(I) Following is a form readable by MAGMA:

g:=Graph<136|{ {64, 71}, {65, 72}, {67, 74}, {66, 73}, {68, 75}, {96, 112}, {102, 118}, {101, 117}, {100, 116}, {99, 115}, {98, 114}, {97, 113}, {96, 113}, {102, 119}, {100, 117}, {98, 115}, {97, 114}, {101, 118}, {99, 116}, {64, 92}, {65, 93}, {66, 94}, {67, 95}, {2, 35}, {30, 63}, {28, 61}, {26, 59}, {24, 57}, {22, 55}, {4, 37}, {6, 39}, {8, 41}, {10, 43}, {12, 45}, {14, 47}, {16, 49}, {18, 51}, {20, 53}, {1, 35}, {29, 63}, {28, 62}, {25, 59}, {24, 58}, {21, 55}, {20, 54}, {4, 38}, {5, 39}, {8, 42}, {9, 43}, {12, 46}, {13, 47}, {16, 50}, {17, 51}, {5, 38}, {29, 62}, {25, 58}, {21, 54}, {9, 42}, {13, 46}, {17, 50}, {68, 96}, {2, 36}, {27, 61}, {26, 60}, {3, 37}, {10, 44}, {11, 45}, {18, 52}, {19, 53}, {3, 36}, {27, 60}, {11, 44}, {19, 52}, {6, 40}, {23, 57}, {22, 56}, {7, 41}, {7, 40}, {95, 112}, {23, 56}, {87, 103}, {95, 111}, {94, 110}, {93, 109}, {92, 108}, {91, 107}, {90, 106}, {89, 105}, {88, 104}, {86, 103}, {94, 111}, {92, 109}, {90, 107}, {88, 105}, {69, 119}, {72, 122}, {73, 123}, {76, 126}, {77, 127}, {72, 123}, {93, 110}, {89, 106}, {76, 127}, {73, 124}, {75, 126}, {74, 124}, {75, 125}, {74, 125}, {91, 108}, {69, 120}, {71, 122}, {14, 48}, {15, 49}, {70, 120}, {71, 121}, {15, 48}, {70, 121}, {87, 104}, {35, 97}, {38, 100}, {39, 101}, {1, 68}, {36, 98}, {37, 99}, {32, 106}, {33, 107}, {34, 108}, {40, 102}, {55, 96}, {56, 97}, {58, 99}, {60, 101}, {57, 98}, {61, 102}, {30, 64}, {31, 65}, {31, 64}, {32, 127}, {59, 100}, {9, 104}, {32, 65}, {31, 126}, {29, 124}, {27, 122}, {25, 120}, {23, 118}, {21, 116}, {11, 106}, {13, 108}, {15, 110}, {17, 112}, {19, 114}, {34, 67}, {32, 66}, {33, 67}, {10, 105}, {30, 125}, {26, 121}, {22, 117}, {14, 109}, {18, 113}, {33, 66}, {44, 72}, {45, 73}, {46, 74}, {47, 75}, {52, 80}, {53, 81}, {54, 82}, {55, 83}, {60, 88}, {61, 89}, {62, 90}, {63, 91}, {34, 68}, {12, 107}, {28, 123}, {20, 115}, {36, 77}, {38, 79}, {48, 89}, {50, 91}, {52, 93}, {54, 95}, {37, 78}, {49, 90}, {53, 94}, {1, 109}, {2, 110}, {3, 111}, {16, 124}, {17, 125}, {18, 126}, {19, 127}, {41, 69}, {42, 70}, {43, 71}, {56, 84}, {57, 85}, {58, 86}, {59, 87}, {8, 103}, {24, 119}, {35, 76}, {51, 92}, {4, 112}, {5, 113}, {6, 114}, {7, 115}, {12, 120}, {13, 121}, {14, 122}, {15, 123}, {30, 104}, {31, 105}, {39, 80}, {47, 88}, {40, 81}, {42, 83}, {44, 85}, {46, 87}, {63, 70}, {29, 103}, {41, 82}, {45, 86}, {62, 69}, {8, 116}, {9, 117}, {10, 118}, {11, 119}, {48, 76}, {49, 77}, {50, 78}, {51, 79}, {16, 111}, {43, 84}, {2, 131}, {4, 133}, {6, 135}, {1, 130}, {5, 134}, {3, 132}, {7, 136}, {20, 128}, {28, 136}, {23, 131}, {22, 130}, {21, 129}, {24, 132}, {27, 135}, {26, 134}, {25, 133}, {33, 128}, {34, 129}, {77, 128}, {79, 130}, {78, 128}, {79, 129}, {78, 129}, {80, 130}, {81, 131}, {84, 134}, {85, 135}, {80, 131}, {84, 135}, {81, 132}, {83, 134}, {82, 132}, {83, 133}, {82, 133}, {85, 136}, {86, 136} }>;

(II) A more general form is to represent the graph as the orbit of {64, 71} under the group generated by the following permutations:

a: (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34)(35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68)(69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102)(103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136)
b: (2, 22, 34, 14)(3, 9, 33, 27)(4, 30, 32, 6)(5, 17, 31, 19)(7, 25, 29, 11)(8, 12, 28, 24)(10, 20, 26, 16)(13, 15, 23, 21)(35, 130, 68, 109)(36, 117, 67, 122)(37, 104, 66, 135)(38, 125, 65, 114)(39, 112, 64, 127)(40, 133, 63, 106)(41, 120, 62, 119)(42, 107, 61, 132)(43, 128, 60, 111)(44, 115, 59, 124)(45, 136, 58, 103)(46, 123, 57, 116)(47, 110, 56, 129)(48, 131, 55, 108)(49, 118, 54, 121)(50, 105, 53, 134)(51, 126, 52, 113)(70, 90, 102, 82)(71, 77, 101, 95)(72, 98, 100, 74)(73, 85, 99, 87)(75, 93, 97, 79)(76, 80, 96, 92)(78, 88, 94, 84)(81, 83, 91, 89)
c: (1, 35, 2, 36, 3, 37, 4, 38, 5, 39, 6, 40, 7, 41, 8, 42, 9, 43, 10, 44, 11, 45, 12, 46, 13, 47, 14, 48, 15, 49, 16, 50, 17, 51, 18, 52, 19, 53, 20, 54, 21, 55, 22, 56, 23, 57, 24, 58, 25, 59, 26, 60, 27, 61, 28, 62, 29, 63, 30, 64, 31, 65, 32, 66, 33, 67, 34, 68)(69, 103, 70, 104, 71, 105, 72, 106, 73, 107, 74, 108, 75, 109, 76, 110, 77, 111, 78, 112, 79, 113, 80, 114, 81, 115, 82, 116, 83, 117, 84, 118, 85, 119, 86, 120, 87, 121, 88, 122, 89, 123, 90, 124, 91, 125, 92, 126, 93, 127, 94, 128, 95, 129, 96, 130, 97, 131, 98, 132, 99, 133, 100, 134, 101, 135, 102, 136)

(III) Last is Groups&Graphs. Copy everything between (not including) the lines of asterisks into a plain text file and save it as "graph.txt". Then launch G&G (Groups&Graphs) and select Read Text from the File menu.

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&Graph
C4[ 136, 9 ]
136
-1 35 68 130 109
-2 110 35 36 131
-3 132 111 36 37
-4 133 112 37 38
-5 134 113 38 39
-6 135 114 39 40
-7 136 115 40 41
-8 103 116 41 42
-9 104 117 42 43
-10 44 105 118 43
-11 44 45 106 119
-12 45 46 107 120
-13 121 46 47 108
-14 122 47 48 109
-15 110 123 48 49
-16 111 124 49 50
-17 112 125 50 51
-18 113 126 51 52
-19 114 127 52 53
-20 115 128 53 54
-21 55 116 129 54
-22 55 56 117 130
-23 56 57 118 131
-24 132 57 58 119
-25 133 58 59 120
-26 121 134 59 60
-27 122 135 60 61
-28 123 136 61 62
-29 124 103 62 63
-30 125 104 63 64
-31 126 105 64 65
-32 66 127 106 65
-33 66 67 128 107
-34 67 68 129 108
-35 1 2 97 76
-36 77 2 3 98
-37 99 78 3 4
-38 100 79 4 5
-39 101 80 5 6
-40 102 81 6 7
-41 69 82 7 8
-42 70 83 8 9
-43 71 84 9 10
-44 11 72 85 10
-45 11 12 73 86
-46 12 13 74 87
-47 88 13 14 75
-48 89 14 15 76
-49 77 90 15 16
-50 78 91 16 17
-51 79 92 17 18
-52 80 93 18 19
-53 81 94 19 20
-54 82 95 20 21
-55 22 83 96 21
-56 22 23 84 97
-57 23 24 85 98
-58 99 24 25 86
-59 100 25 26 87
-60 88 101 26 27
-61 89 102 27 28
-62 90 69 28 29
-63 91 70 29 30
-64 92 71 30 31
-65 93 72 31 32
-66 33 94 73 32
-67 33 34 95 74
-68 1 34 96 75
-69 62 41 119 120
-70 121 63 42 120
-71 121 122 64 43
-72 44 122 123 65
-73 66 45 123 124
-74 67 46 124 125
-75 68 47 125 126
-76 35 48 126 127
-77 36 49 127 128
-78 37 50 128 129
-79 38 51 129 130
-80 39 52 130 131
-81 132 40 53 131
-82 132 133 41 54
-83 55 133 134 42
-84 56 134 135 43
-85 44 57 135 136
-86 45 58 103 136
-87 46 59 103 104
-88 47 60 104 105
-89 48 61 105 106
-90 49 62 106 107
-91 50 63 107 108
-92 51 64 108 109
-93 110 52 65 109
-94 66 110 111 53
-95 67 111 112 54
-96 55 68 112 113
-97 56 35 113 114
-98 57 36 114 115
-99 58 37 115 116
-100 59 38 116 117
-101 60 39 117 118
-102 61 40 118 119
-103 29 8 86 87
-104 88 30 9 87
-105 88 89 31 10
-106 11 89 90 32
-107 33 12 90 91
-108 34 13 91 92
-109 1 14 92 93
-110 2 15 93 94
-111 3 16 94 95
-112 4 17 95 96
-113 5 18 96 97
-114 6 19 97 98
-115 99 7 20 98
-116 99 100 8 21
-117 22 100 101 9
-118 23 101 102 10
-119 11 24 69 102
-120 12 25 69 70
-121 13 26 70 71
-122 14 27 71 72
-123 15 28 72 73
-124 16 29 73 74
-125 17 30 74 75
-126 18 31 75 76
-127 77 19 32 76
-128 33 77 78 20
-129 34 78 79 21
-130 22 1 79 80
-131 23 2 80 81
-132 24 3 81 82
-133 25 4 82 83
-134 26 5 83 84
-135 27 6 84 85
-136 28 7 85 86
0

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