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On this page are computer-accessible forms for the graph C4[ 144, 11 ] = MPS(12,24;5).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {24, 27} under the group generated by the following permutations:

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

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