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On this page are computer-accessible forms for the graph C4[ 144, 64 ] = BGCG({4,4}_6,6;K1;{13,16}).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {68, 73} under the group generated by the following permutations:

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

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

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