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On this page are computer-accessible forms for the graph C4[ 156, 6 ] = PS(12,13;3).

(I) Following is a form readable by MAGMA:

g:=Graph<156|{ {52, 53}, {130, 131}, {13, 14}, {64, 67}, {24, 27}, {104, 107}, {75, 79}, {114, 118}, {115, 119}, {25, 28}, {65, 68}, {26, 29}, {91, 92}, {32, 41}, {70, 79}, {34, 43}, {36, 45}, {38, 47}, {112, 121}, {114, 123}, {116, 125}, {17, 27}, {65, 75}, {64, 74}, {20, 30}, {21, 31}, {96, 106}, {97, 107}, {100, 110}, {101, 111}, {33, 42}, {37, 46}, {113, 122}, {117, 126}, {2, 14}, {80, 92}, {51, 63}, {50, 62}, {49, 61}, {48, 60}, {3, 15}, {36, 40}, {37, 41}, {38, 42}, {39, 43}, {81, 93}, {82, 94}, {83, 95}, {116, 120}, {117, 121}, {128, 140}, {129, 141}, {130, 142}, {103, 106}, {1, 15}, {80, 94}, {49, 63}, {48, 62}, {18, 28}, {19, 29}, {81, 95}, {98, 108}, {99, 109}, {128, 142}, {129, 143}, {35, 44}, {102, 105}, {115, 124}, {14, 30}, {140, 156}, {139, 155}, {138, 154}, {15, 31}, {96, 112}, {97, 113}, {98, 114}, {99, 115}, {100, 116}, {101, 117}, {131, 147}, {132, 148}, {133, 149}, {134, 150}, {135, 151}, {136, 152}, {137, 153}, {32, 49}, {74, 91}, {72, 89}, {70, 87}, {68, 85}, {66, 83}, {34, 51}, {106, 123}, {108, 125}, {110, 127}, {2, 16}, {79, 93}, {47, 61}, {46, 60}, {3, 17}, {6, 20}, {7, 21}, {10, 24}, {11, 25}, {42, 56}, {43, 57}, {33, 50}, {73, 90}, {69, 86}, {105, 122}, {109, 126}, {4, 16}, {47, 59}, {46, 58}, {5, 17}, {6, 18}, {7, 19}, {12, 24}, {13, 25}, {44, 56}, {45, 57}, {4, 18}, {143, 153}, {142, 152}, {45, 59}, {5, 19}, {12, 26}, {44, 58}, {102, 112}, {103, 113}, {105, 127}, {134, 144}, {135, 145}, {35, 52}, {71, 80}, {67, 84}, {39, 48}, {107, 124}, {111, 120}, {72, 81}, {78, 87}, {76, 85}, {74, 83}, {110, 119}, {131, 154}, {133, 156}, {66, 88}, {141, 151}, {140, 150}, {67, 89}, {104, 114}, {136, 146}, {137, 147}, {1, 26}, {77, 86}, {73, 82}, {109, 118}, {8, 20}, {78, 82}, {77, 81}, {76, 80}, {9, 21}, {10, 22}, {11, 23}, {41, 53}, {42, 54}, {43, 55}, {141, 144}, {143, 146}, {8, 22}, {139, 149}, {69, 91}, {68, 90}, {9, 23}, {40, 54}, {41, 55}, {138, 148}, {71, 88}, {142, 145}, {75, 84}, {132, 155}, {79, 104}, {15, 38}, {93, 116}, {27, 49}, {30, 52}, {14, 37}, {94, 117}, {28, 50}, {29, 51}, {31, 48}, {92, 115}, {16, 32}, {17, 33}, {18, 34}, {19, 35}, {20, 36}, {21, 37}, {22, 38}, {23, 39}, {92, 108}, {93, 109}, {94, 110}, {95, 111}, {28, 45}, {30, 47}, {82, 96}, {83, 97}, {86, 100}, {87, 101}, {90, 104}, {29, 46}, {84, 96}, {85, 97}, {86, 98}, {87, 99}, {22, 32}, {23, 33}, {84, 98}, {85, 99}, {95, 105}, {16, 39}, {27, 44}, {31, 40}, {24, 34}, {25, 35}, {88, 100}, {89, 101}, {90, 102}, {91, 103}, {26, 36}, {88, 102}, {89, 103}, {40, 65}, {53, 69}, {62, 78}, {61, 77}, {60, 76}, {59, 75}, {58, 74}, {57, 73}, {56, 72}, {55, 71}, {54, 70}, {50, 64}, {51, 65}, {52, 64}, {62, 72}, {63, 73}, {53, 76}, {55, 78}, {56, 66}, {61, 71}, {60, 70}, {57, 67}, {54, 77}, {63, 66}, {58, 68}, {59, 69}, {4, 151}, {8, 155}, {1, 148}, {3, 150}, {5, 144}, {7, 146}, {9, 156}, {13, 152}, {2, 149}, {6, 145}, {1, 153}, {2, 154}, {3, 155}, {4, 156}, {10, 144}, {11, 145}, {8, 147}, {12, 151}, {5, 152}, {7, 154}, {9, 148}, {11, 150}, {12, 146}, {13, 147}, {6, 153}, {10, 149}, {106, 128}, {107, 129}, {108, 130}, {111, 128}, {112, 129}, {118, 132}, {119, 133}, {122, 136}, {123, 137}, {126, 140}, {127, 141}, {113, 130}, {119, 131}, {124, 136}, {125, 137}, {126, 138}, {127, 139}, {124, 138}, {125, 139}, {118, 143}, {120, 132}, {121, 133}, {122, 134}, {123, 135}, {120, 134}, {121, 135} }>;

(II) A more general form is to represent the graph as the orbit of {52, 53} under the group generated by the following permutations:

a: (1, 14, 27, 40, 53, 66, 79, 92, 105, 118, 131, 144)(2, 17, 36, 41, 56, 75, 80, 95, 114, 119, 134, 153)(3, 20, 32, 42, 59, 71, 81, 98, 110, 120, 137, 149)(4, 23, 28, 43, 62, 67, 82, 101, 106, 121, 140, 145)(5, 26, 37, 44, 65, 76, 83, 104, 115, 122, 143, 154)(6, 16, 33, 45, 55, 72, 84, 94, 111, 123, 133, 150)(7, 19, 29, 46, 58, 68, 85, 97, 107, 124, 136, 146)(8, 22, 38, 47, 61, 77, 86, 100, 116, 125, 139, 155)(9, 25, 34, 48, 64, 73, 87, 103, 112, 126, 142, 151)(10, 15, 30, 49, 54, 69, 88, 93, 108, 127, 132, 147)(11, 18, 39, 50, 57, 78, 89, 96, 117, 128, 135, 156)(12, 21, 35, 51, 60, 74, 90, 99, 113, 129, 138, 152)(13, 24, 31, 52, 63, 70, 91, 102, 109, 130, 141, 148)
b: (2, 13)(3, 12)(4, 11)(5, 10)(6, 9)(7, 8)(15, 26)(16, 25)(17, 24)(18, 23)(19, 22)(20, 21)(28, 39)(29, 38)(30, 37)(31, 36)(32, 35)(33, 34)(41, 52)(42, 51)(43, 50)(44, 49)(45, 48)(46, 47)(54, 65)(55, 64)(56, 63)(57, 62)(58, 61)(59, 60)(67, 78)(68, 77)(69, 76)(70, 75)(71, 74)(72, 73)(80, 91)(81, 90)(82, 89)(83, 88)(84, 87)(85, 86)(93, 104)(94, 103)(95, 102)(96, 101)(97, 100)(98, 99)(106, 117)(107, 116)(108, 115)(109, 114)(110, 113)(111, 112)(119, 130)(120, 129)(121, 128)(122, 127)(123, 126)(124, 125)(132, 143)(133, 142)(134, 141)(135, 140)(136, 139)(137, 138)(145, 156)(146, 155)(147, 154)(148, 153)(149, 152)(150, 151)
c: (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, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156)

(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[ 156, 6 ]
156
-1 15 26 148 153
-2 154 14 16 149
-3 155 15 17 150
-4 156 16 18 151
-5 144 17 19 152
-6 145 18 20 153
-7 154 146 19 21
-8 22 155 147 20
-9 23 156 148 21
-10 22 144 24 149
-11 23 145 25 150
-12 24 146 26 151
-13 14 25 147 152
-14 2 13 37 30
-15 1 3 38 31
-16 2 4 39 32
-17 33 3 5 27
-18 34 4 6 28
-19 35 5 7 29
-20 36 6 8 30
-21 37 7 9 31
-22 38 8 10 32
-23 11 33 39 9
-24 12 34 27 10
-25 11 13 35 28
-26 1 12 36 29
-27 44 24 49 17
-28 45 25 50 18
-29 46 26 51 19
-30 14 47 52 20
-31 15 48 40 21
-32 22 16 49 41
-33 23 17 50 42
-34 24 18 51 43
-35 44 25 19 52
-36 45 26 40 20
-37 46 14 41 21
-38 22 47 15 42
-39 23 48 16 43
-40 36 31 54 65
-41 55 37 53 32
-42 33 56 38 54
-43 55 34 57 39
-44 56 35 58 27
-45 57 36 59 28
-46 58 37 60 29
-47 59 38 61 30
-48 60 39 62 31
-49 27 61 63 32
-50 33 28 62 64
-51 34 29 63 65
-52 35 30 53 64
-53 69 41 52 76
-54 77 70 40 42
-55 78 71 41 43
-56 44 66 72 42
-57 45 67 73 43
-58 44 46 68 74
-59 45 47 69 75
-60 46 48 70 76
-61 77 47 49 71
-62 78 48 50 72
-63 66 49 51 73
-64 67 50 52 74
-65 68 40 51 75
-66 88 56 83 63
-67 89 57 84 64
-68 90 58 85 65
-69 91 59 53 86
-70 79 60 54 87
-71 55 88 80 61
-72 56 89 81 62
-73 57 90 82 63
-74 58 91 83 64
-75 79 59 84 65
-76 80 60 85 53
-77 81 61 86 54
-78 55 82 62 87
-79 70 93 104 75
-80 92 71 94 76
-81 77 93 72 95
-82 78 94 73 96
-83 66 95 74 97
-84 67 96 75 98
-85 99 68 97 76
-86 77 100 69 98
-87 99 78 101 70
-88 66 100 102 71
-89 67 101 103 72
-90 68 102 104 73
-91 69 92 103 74
-92 80 91 115 108
-93 79 81 116 109
-94 110 80 82 117
-95 111 81 83 105
-96 112 82 84 106
-97 113 83 85 107
-98 114 84 86 108
-99 115 85 87 109
-100 88 110 116 86
-101 89 111 117 87
-102 88 90 112 105
-103 89 91 113 106
-104 79 90 114 107
-105 122 102 127 95
-106 123 103 128 96
-107 124 104 129 97
-108 92 125 130 98
-109 99 93 126 118
-110 100 94 127 119
-111 101 95 128 120
-112 121 102 96 129
-113 122 103 97 130
-114 123 104 118 98
-115 99 124 92 119
-116 100 125 93 120
-117 121 101 126 94
-118 132 143 114 109
-119 110 133 115 131
-120 132 111 134 116
-121 133 112 135 117
-122 134 113 136 105
-123 135 114 137 106
-124 136 115 138 107
-125 137 116 139 108
-126 138 117 140 109
-127 110 105 139 141
-128 111 106 140 142
-129 143 112 107 141
-130 113 108 131 142
-131 154 147 119 130
-132 155 148 118 120
-133 121 156 149 119
-134 122 144 150 120
-135 121 123 145 151
-136 122 124 146 152
-137 123 125 147 153
-138 154 124 126 148
-139 155 125 127 149
-140 156 126 128 150
-141 144 127 129 151
-142 145 128 130 152
-143 146 118 129 153
-144 134 5 141 10
-145 11 135 6 142
-146 143 12 136 7
-147 13 137 8 131
-148 132 1 138 9
-149 133 2 139 10
-150 11 134 3 140
-151 12 135 4 141
-152 13 136 5 142
-153 143 1 137 6
-154 2 138 7 131
-155 132 3 139 8
-156 133 4 140 9
0

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