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On this page are computer-accessible forms for the graph C4[ 144, 6 ] = {4,4}_[12,6].

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {2, 3} under the group generated by the following permutations:

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

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

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