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On this page are computer-accessible forms for the graph C4[ 156, 9 ] = PS(6,52;3).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {52, 54} under the group generated by the following permutations:

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

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