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On this page are computer-accessible forms for the graph C4[ 136, 12 ] = PL(MC3(4,17,1,16,4,0,1),[4^17,34^2]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {65, 77} under the group generated by the following permutations:

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

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

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