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On this page are computer-accessible forms for the graph C4[ 144, 29 ] = AMC(4,12,[9.5:4.9]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {64, 73} under the group generated by the following permutations:

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

(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.

**************

&Graph
C4[ 144, 29 ]
144
-1 67 37 136 117
-2 68 38 137 118
-3 69 39 138 119
-4 133 70 40 120
-5 134 71 115 41
-6 135 72 116 42
-7 123 37 43 142
-8 44 143 124 38
-9 45 144 125 39
-10 46 126 40 139
-11 121 47 41 140
-12 122 48 42 141
-13 112 49 129 43
-14 44 113 50 130
-15 45 114 51 131
-16 132 46 52 109
-17 110 47 127 53
-18 111 48 128 54
-19 55 135 49 118
-20 56 136 50 119
-21 57 137 51 120
-22 58 115 138 52
-23 133 59 116 53
-24 134 60 117 54
-25 55 124 61 141
-26 56 125 62 142
-27 143 57 126 63
-28 121 144 58 64
-29 122 59 139 65
-30 66 123 60 140
-31 67 111 61 130
-32 68 112 62 131
-33 132 69 113 63
-34 70 114 127 64
-35 71 128 65 109
-36 66 110 72 129
-37 88 1 105 7
-38 89 2 106 8
-39 90 3 107 9
-40 4 85 108 10
-41 11 103 5 86
-42 12 104 6 87
-43 13 94 7 75
-44 14 95 8 76
-45 77 15 96 9
-46 78 91 16 10
-47 11 92 17 73
-48 12 93 18 74
-49 100 13 81 19
-50 101 14 82 20
-51 102 15 83 21
-52 22 16 84 97
-53 23 79 17 98
-54 99 24 80 18
-55 25 106 19 87
-56 88 26 107 20
-57 89 27 108 21
-58 22 90 103 28
-59 23 104 29 85
-60 24 105 30 86
-61 25 93 31 76
-62 77 26 94 32
-63 33 78 27 95
-64 34 28 73 96
-65 35 91 29 74
-66 36 92 30 75
-67 99 1 82 31
-68 100 2 83 32
-69 33 101 3 84
-70 34 79 102 4
-71 35 80 5 97
-72 36 81 6 98
-73 47 124 64 130
-74 48 125 65 131
-75 66 132 126 43
-76 44 121 61 127
-77 45 122 62 128
-78 46 123 63 129
-79 70 136 53 130
-80 71 137 54 131
-81 132 49 72 138
-82 67 133 50 127
-83 68 134 51 128
-84 69 135 52 129
-85 59 136 40 142
-86 143 60 137 41
-87 55 144 138 42
-88 56 133 37 139
-89 57 134 38 140
-90 58 135 39 141
-91 46 112 65 142
-92 66 143 47 113
-93 144 48 114 61
-94 62 139 43 109
-95 44 110 63 140
-96 45 111 64 141
-97 112 71 52 118
-98 113 72 53 119
-99 67 114 54 120
-100 68 49 115 109
-101 110 69 50 116
-102 111 70 51 117
-103 58 124 41 118
-104 59 125 42 119
-105 37 60 126 120
-106 55 121 38 115
-107 56 122 39 116
-108 57 123 40 117
-109 100 35 16 94
-110 101 36 17 95
-111 102 18 96 31
-112 13 91 97 32
-113 33 14 92 98
-114 99 34 15 93
-115 22 100 5 106
-116 23 101 6 107
-117 1 24 102 108
-118 2 103 19 97
-119 3 104 20 98
-120 99 4 105 21
-121 11 28 106 76
-122 77 12 29 107
-123 78 7 30 108
-124 25 103 73 8
-125 26 104 74 9
-126 27 105 75 10
-127 34 82 17 76
-128 77 35 83 18
-129 78 13 36 84
-130 79 14 73 31
-131 80 15 74 32
-132 33 81 16 75
-133 88 23 4 82
-134 89 24 5 83
-135 90 6 84 19
-136 1 79 85 20
-137 2 80 86 21
-138 22 3 81 87
-139 88 94 29 10
-140 11 89 95 30
-141 12 90 25 96
-142 91 26 7 85
-143 92 27 8 86
-144 93 28 9 87
0

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