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On this page are computer-accessible forms for the graph C4[ 144, 63 ] = BGCG({4,4}_6,6;K1;{2,5}).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {69, 77} under the group generated by the following permutations:

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

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

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