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On this page are computer-accessible forms for the graph C4[ 144, 27 ] = AMC(16,3,[0.1:1.2]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {36, 37} under the group generated by the following permutations:

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

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