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On this page are computer-accessible forms for the graph C4[ 144, 68 ] = BGCG(AMC(8,3,[0.1:1.2]);K1;7).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {68, 77} under the group generated by the following permutations:

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

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

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