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On this page are computer-accessible forms for the graph C4[ 144, 66 ] = BGCG(AMC(8,3,[0.1:1.2]);K1;2).

(I) Following is a form readable by MAGMA:

g:=Graph<144|{ {70, 78}, {64, 75}, {65, 77}, {71, 87}, {70, 84}, {71, 95}, {68, 93}, {70, 90}, {64, 94}, {69, 91}, {69, 96}, {72, 109}, {64, 102}, {66, 107}, {70, 111}, {66, 104}, {68, 110}, {67, 108}, {72, 120}, {67, 114}, {71, 118}, {64, 117}, {66, 116}, {71, 112}, {68, 127}, {72, 115}, {65, 125}, {67, 124}, {10, 74}, {39, 103}, {18, 82}, {45, 109}, {30, 95}, {37, 100}, {55, 118}, {34, 96}, {63, 125}, {58, 120}, {36, 102}, {24, 91}, {37, 102}, {25, 90}, {50, 113}, {18, 86}, {30, 90}, {23, 83}, {21, 81}, {40, 108}, {51, 119}, {56, 124}, {10, 76}, {22, 80}, {47, 105}, {56, 126}, {14, 73}, {28, 91}, {6, 78}, {32, 104}, {31, 87}, {26, 82}, {29, 84}, {40, 97}, {34, 107}, {19, 89}, {42, 96}, {6, 77}, {62, 117}, {46, 101}, {34, 110}, {60, 112}, {19, 94}, {58, 119}, {32, 109}, {5, 75}, {43, 101}, {32, 111}, {52, 123}, {53, 122}, {54, 121}, {5, 85}, {6, 86}, {46, 126}, {57, 105}, {24, 73}, {35, 114}, {33, 112}, {4, 87}, {61, 110}, {59, 104}, {39, 116}, {15, 92}, {9, 93}, {62, 106}, {59, 111}, {27, 79}, {51, 103}, {54, 98}, {12, 89}, {49, 100}, {52, 97}, {2, 84}, {61, 107}, {35, 117}, {14, 88}, {41, 127}, {35, 116}, {52, 99}, {21, 76}, {36, 125}, {2, 88}, {11, 81}, {40, 114}, {3, 95}, {63, 99}, {62, 98}, {38, 122}, {15, 83}, {44, 113}, {11, 85}, {39, 121}, {37, 123}, {20, 74}, {14, 80}, {45, 115}, {52, 106}, {3, 92}, {16, 79}, {4, 100}, {17, 113}, {57, 89}, {6, 103}, {29, 124}, {48, 81}, {49, 80}, {50, 83}, {60, 94}, {27, 120}, {28, 127}, {57, 90}, {1, 101}, {12, 105}, {43, 78}, {47, 74}, {51, 86}, {7, 97}, {19, 117}, {7, 96}, {31, 120}, {50, 85}, {53, 82}, {5, 109}, {20, 125}, {56, 81}, {22, 124}, {28, 118}, {26, 112}, {12, 103}, {59, 80}, {38, 77}, {32, 75}, {13, 97}, {33, 77}, {26, 118}, {48, 92}, {55, 91}, {19, 126}, {63, 82}, {10, 100}, {37, 75}, {3, 108}, {60, 83}, {33, 78}, {28, 115}, {24, 119}, {9, 102}, {9, 121}, {10, 123}, {18, 99}, {11, 122}, {41, 88}, {1, 115}, {61, 79}, {59, 73}, {30, 108}, {8, 122}, {17, 98}, {38, 85}, {25, 106}, {44, 95}, {5, 113}, {41, 93}, {11, 126}, {16, 101}, {12, 121}, {25, 111}, {42, 92}, {46, 89}, {47, 88}, {23, 110}, {36, 93}, {27, 98}, {54, 79}, {8, 114}, {25, 99}, {13, 119}, {51, 73}, {17, 106}, {44, 87}, {45, 86}, {55, 76}, {7, 123}, {8, 116}, {48, 76}, {20, 105}, {21, 104}, {55, 74}, {1, 127}, {21, 107}, {33, 94}, {43, 84}, {4, 132}, {2, 128}, {13, 139}, {4, 131}, {15, 135}, {1, 139}, {15, 133}, {2, 136}, {7, 140}, {9, 133}, {13, 129}, {3, 141}, {26, 138}, {31, 143}, {22, 135}, {23, 134}, {27, 137}, {16, 131}, {22, 130}, {29, 137}, {23, 129}, {24, 142}, {8, 144}, {30, 134}, {17, 136}, {16, 138}, {20, 143}, {31, 132}, {29, 128}, {14, 144}, {18, 141}, {45, 141}, {39, 132}, {40, 139}, {44, 136}, {46, 139}, {53, 144}, {36, 130}, {47, 136}, {43, 131}, {38, 140}, {42, 128}, {35, 142}, {34, 140}, {42, 133}, {62, 142}, {56, 137}, {49, 131}, {50, 129}, {54, 133}, {58, 143}, {49, 135}, {61, 138}, {41, 144}, {58, 129}, {60, 135}, {48, 141}, {63, 130}, {53, 138}, {57, 134}, {67, 130}, {72, 137}, {68, 134}, {69, 128}, {66, 132}, {69, 142}, {65, 140}, {65, 143} }>;

(II) A more general form is to represent the graph as the orbit of {70, 78} under the group generated by the following permutations:

a: (2, 8, 3, 6)(4, 9, 7, 5)(10, 64)(11, 71, 12, 69)(13, 72, 16, 68)(14, 67, 18, 70)(15, 65, 17, 66)(19, 55)(20, 62, 21, 60)(22, 63, 25, 59)(23, 58, 27, 61)(24, 56, 26, 57)(28, 46)(29, 53, 30, 51)(31, 54, 34, 50)(32, 49, 36, 52)(33, 47, 35, 48)(38, 44, 39, 42)(40, 45, 43, 41)(73, 124, 82, 90)(74, 117, 76, 94)(75, 100, 102, 123)(77, 136, 116, 92)(78, 88, 114, 141)(79, 110, 129, 120)(80, 130, 99, 111)(81, 112, 105, 142)(83, 143, 98, 107)(84, 144, 108, 86)(85, 87, 121, 96)(89, 91, 126, 118)(93, 97, 109, 131)(95, 103, 128, 122)(101, 127, 139, 115)(104, 135, 125, 106)(113, 132, 133, 140)(119, 137, 138, 134)
b: (1, 10)(2, 18)(3, 14)(4, 13)(5, 12)(6, 17)(7, 16)(8, 15)(9, 11)(19, 64)(20, 72)(21, 68)(22, 67)(23, 66)(24, 71)(25, 70)(26, 69)(27, 65)(28, 55)(29, 63)(30, 59)(31, 58)(32, 57)(33, 62)(34, 61)(35, 60)(36, 56)(37, 46)(38, 54)(39, 50)(40, 49)(41, 48)(42, 53)(43, 52)(44, 51)(45, 47)(73, 95)(74, 115)(75, 89)(76, 127)(77, 98)(78, 106)(79, 140)(80, 108)(81, 93)(82, 128)(83, 116)(84, 99)(85, 121)(86, 136)(87, 119)(88, 141)(90, 111)(91, 118)(92, 144)(94, 117)(96, 138)(97, 131)(100, 139)(101, 123)(102, 126)(103, 113)(104, 134)(105, 109)(107, 110)(112, 142)(114, 135)(120, 143)(122, 133)(124, 130)(125, 137)(129, 132)
c: (1, 2, 9, 8)(3, 4, 7, 6)(10, 65, 18, 71)(11, 72, 17, 64)(12, 67, 16, 69)(13, 70, 15, 66)(14, 68)(19, 56, 27, 62)(20, 63, 26, 55)(21, 58, 25, 60)(22, 61, 24, 57)(23, 59)(28, 47, 36, 53)(29, 54, 35, 46)(30, 49, 34, 51)(31, 52, 33, 48)(32, 50)(37, 38, 45, 44)(39, 40, 43, 42)(73, 134, 80, 110)(74, 125, 82, 118)(75, 85, 109, 113)(76, 143, 99, 112)(77, 141, 87, 123)(78, 92, 132, 97)(79, 142, 89, 124)(81, 120, 106, 94)(83, 104, 129, 111)(84, 133, 116, 139)(86, 95, 100, 140)(88, 93, 144, 127)(90, 135, 107, 119)(91, 105, 130, 138)(96, 103, 108, 131)(98, 117, 126, 137)(101, 128, 121, 114)(102, 122, 115, 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[ 144, 66 ]
144
-1 101 115 127 139
-2 88 136 84 128
-3 92 95 108 141
-4 132 100 87 131
-5 113 85 75 109
-6 77 78 103 86
-7 123 96 140 97
-8 122 144 114 116
-9 121 133 102 93
-10 100 123 74 76
-11 122 81 126 85
-12 121 89 103 105
-13 139 129 97 119
-14 88 144 80 73
-15 133 135 92 83
-16 79 101 138 131
-17 113 136 106 98
-18 99 82 86 141
-19 89 126 94 117
-20 143 125 105 74
-21 81 104 107 76
-22 80 124 135 130
-23 110 134 83 129
-24 91 73 119 142
-25 99 111 90 106
-26 112 82 138 118
-27 79 137 98 120
-28 91 115 127 118
-29 124 137 84 128
-30 90 134 95 108
-31 132 143 87 120
-32 111 104 75 109
-33 77 78 112 94
-34 110 96 107 140
-35 114 116 117 142
-36 102 125 93 130
-37 100 123 102 75
-38 77 122 85 140
-39 121 132 103 116
-40 114 139 97 108
-41 88 144 93 127
-42 133 92 128 96
-43 78 101 84 131
-44 113 136 95 87
-45 115 86 141 109
-46 89 101 126 139
-47 88 136 105 74
-48 81 92 141 76
-49 100 80 135 131
-50 113 83 85 129
-51 103 73 86 119
-52 99 123 106 97
-53 122 144 82 138
-54 121 133 79 98
-55 91 74 118 76
-56 124 81 126 137
-57 89 90 134 105
-58 143 129 119 120
-59 111 80 104 73
-60 112 135 83 94
-61 110 79 138 107
-62 106 117 98 142
-63 99 125 82 130
-64 102 94 117 75
-65 77 143 125 140
-66 132 104 116 107
-67 124 114 108 130
-68 110 134 93 127
-69 91 128 96 142
-70 78 111 90 84
-71 112 95 118 87
-72 115 137 109 120
-73 24 14 59 51
-74 55 47 20 10
-75 37 5 64 32
-76 55 48 10 21
-77 33 38 6 65
-78 33 70 6 43
-79 16 27 61 54
-80 22 14 59 49
-81 11 56 48 21
-82 26 18 63 53
-83 23 15 60 50
-84 2 70 29 43
-85 11 5 38 50
-86 45 6 18 51
-87 44 4 71 31
-88 2 14 47 41
-89 12 46 57 19
-90 57 25 70 30
-91 55 24 69 28
-92 3 15 48 42
-93 68 36 41 9
-94 33 60 19 64
-95 44 3 71 30
-96 34 69 7 42
-97 13 7 40 52
-98 27 17 62 54
-99 25 18 52 63
-100 4 37 49 10
-101 1 46 16 43
-102 36 37 9 64
-103 12 6 39 51
-104 66 59 21 32
-105 12 57 47 20
-106 25 17 62 52
-107 66 34 61 21
-108 67 3 40 30
-109 45 5 72 32
-110 23 34 68 61
-111 25 59 70 32
-112 33 26 60 71
-113 44 5 17 50
-114 67 35 40 8
-115 1 45 28 72
-116 66 35 39 8
-117 35 62 19 64
-118 55 26 71 28
-119 13 24 58 51
-120 58 27 72 31
-121 12 39 9 54
-122 11 38 8 53
-123 37 7 52 10
-124 22 56 67 29
-125 36 63 20 65
-126 11 56 46 19
-127 1 68 28 41
-128 2 69 29 42
-129 23 13 58 50
-130 22 67 36 63
-131 4 16 49 43
-132 66 4 39 31
-133 15 9 42 54
-134 23 57 68 30
-135 22 15 49 60
-136 44 2 47 17
-137 56 27 72 29
-138 26 16 61 53
-139 1 13 46 40
-140 34 38 7 65
-141 45 3 48 18
-142 24 35 69 62
-143 58 20 31 65
-144 14 8 41 53
0

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