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On this page are computer-accessible forms for the graph C4[ 168, 15 ] = PS(6,56;3).

(I) Following is a form readable by MAGMA:

g:=Graph<168|{ {56, 58}, {81, 85}, {82, 86}, {83, 87}, {84, 88}, {129, 141}, {130, 142}, {131, 143}, {55, 57}, {112, 126}, {112, 127}, {128, 143}, {99, 114}, {139, 154}, {137, 152}, {135, 150}, {101, 116}, {103, 118}, {105, 120}, {107, 122}, {109, 124}, {111, 126}, {129, 144}, {131, 146}, {133, 148}, {99, 113}, {102, 116}, {103, 117}, {106, 120}, {107, 121}, {110, 124}, {111, 125}, {98, 113}, {138, 153}, {102, 117}, {106, 121}, {110, 125}, {130, 145}, {134, 149}, {132, 144}, {140, 152}, {133, 145}, {134, 146}, {135, 147}, {100, 114}, {101, 115}, {108, 122}, {109, 123}, {64, 87}, {140, 155}, {72, 95}, {100, 115}, {108, 123}, {132, 147}, {65, 88}, {69, 92}, {67, 90}, {71, 94}, {4, 31}, {70, 93}, {66, 89}, {36, 63}, {32, 59}, {1, 29}, {139, 151}, {138, 150}, {137, 149}, {136, 148}, {2, 30}, {3, 31}, {3, 30}, {35, 62}, {33, 60}, {32, 62}, {33, 63}, {104, 118}, {105, 119}, {2, 29}, {136, 151}, {68, 91}, {34, 61}, {104, 119}, {64, 96}, {70, 102}, {69, 101}, {68, 100}, {67, 99}, {66, 98}, {65, 97}, {71, 103}, {72, 104}, {73, 105}, {74, 106}, {75, 107}, {76, 108}, {77, 109}, {78, 110}, {79, 111}, {80, 112}, {30, 60}, {31, 61}, {4, 32}, {5, 33}, {6, 34}, {7, 35}, {12, 40}, {13, 41}, {14, 42}, {15, 43}, {20, 48}, {21, 49}, {22, 50}, {23, 51}, {28, 56}, {5, 32}, {31, 58}, {7, 34}, {13, 40}, {15, 42}, {21, 48}, {23, 50}, {29, 59}, {6, 33}, {14, 41}, {22, 49}, {30, 57}, {128, 168}, {73, 96}, {75, 98}, {77, 100}, {79, 102}, {85, 127}, {8, 35}, {12, 39}, {24, 51}, {28, 55}, {74, 97}, {78, 101}, {8, 36}, {9, 37}, {10, 38}, {11, 39}, {24, 52}, {25, 53}, {26, 54}, {27, 55}, {9, 36}, {11, 38}, {25, 52}, {27, 54}, {10, 37}, {26, 53}, {76, 99}, {80, 103}, {1, 56}, {81, 104}, {83, 106}, {16, 43}, {20, 47}, {82, 105}, {16, 44}, {17, 45}, {18, 46}, {19, 47}, {17, 44}, {19, 46}, {18, 45}, {84, 107}, {29, 84}, {61, 112}, {60, 111}, {57, 108}, {59, 110}, {58, 109}, {57, 89}, {63, 95}, {62, 94}, {61, 93}, {60, 92}, {59, 91}, {58, 90}, {34, 64}, {54, 84}, {51, 81}, {50, 80}, {47, 77}, {46, 76}, {43, 73}, {42, 72}, {39, 69}, {38, 68}, {35, 65}, {37, 64}, {55, 82}, {53, 80}, {47, 74}, {45, 72}, {39, 66}, {36, 66}, {53, 83}, {52, 82}, {45, 75}, {44, 74}, {37, 67}, {38, 65}, {54, 81}, {46, 73}, {63, 86}, {40, 67}, {62, 85}, {56, 83}, {44, 71}, {41, 68}, {43, 70}, {40, 70}, {41, 71}, {42, 69}, {48, 75}, {52, 79}, {49, 76}, {51, 78}, {48, 78}, {49, 79}, {50, 77}, {12, 142}, {13, 143}, {16, 146}, {17, 147}, {20, 150}, {21, 151}, {24, 154}, {25, 155}, {28, 158}, {11, 141}, {18, 148}, {19, 149}, {26, 156}, {27, 157}, {23, 144}, {24, 145}, {26, 147}, {28, 149}, {25, 146}, {22, 152}, {23, 153}, {27, 148}, {2, 151}, {8, 157}, {10, 159}, {1, 150}, {9, 158}, {20, 141}, {22, 143}, {3, 152}, {7, 156}, {21, 142}, {4, 153}, {6, 155}, {1, 159}, {14, 144}, {15, 145}, {5, 154}, {2, 160}, {3, 161}, {6, 164}, {7, 165}, {10, 168}, {4, 162}, {5, 163}, {11, 160}, {15, 164}, {12, 161}, {14, 163}, {8, 166}, {9, 167}, {13, 162}, {16, 165}, {18, 167}, {17, 166}, {19, 168}, {85, 128}, {87, 130}, {93, 136}, {95, 138}, {117, 160}, {119, 162}, {125, 168}, {86, 128}, {87, 129}, {94, 136}, {95, 137}, {86, 129}, {94, 137}, {118, 161}, {120, 160}, {121, 161}, {122, 162}, {123, 163}, {124, 164}, {125, 165}, {126, 166}, {127, 167}, {88, 130}, {89, 131}, {92, 134}, {93, 135}, {88, 131}, {92, 135}, {120, 163}, {124, 167}, {89, 132}, {91, 134}, {121, 164}, {123, 166}, {90, 132}, {91, 133}, {90, 133}, {122, 165}, {113, 153}, {114, 154}, {115, 155}, {116, 156}, {117, 157}, {118, 158}, {119, 159}, {96, 138}, {97, 139}, {96, 139}, {116, 159}, {97, 140}, {113, 156}, {115, 158}, {98, 140}, {114, 157}, {127, 142}, {126, 141} }>;

(II) A more general form is to represent the graph as the orbit of {56, 58} under the group generated by the following permutations:

a: (2, 28)(3, 27)(4, 26)(5, 25)(6, 24)(7, 23)(8, 22)(9, 21)(10, 20)(11, 19)(12, 18)(13, 17)(14, 16)(29, 56)(30, 55)(31, 54)(32, 53)(33, 52)(34, 51)(35, 50)(36, 49)(37, 48)(38, 47)(39, 46)(40, 45)(41, 44)(42, 43)(58, 84)(59, 83)(60, 82)(61, 81)(62, 80)(63, 79)(64, 78)(65, 77)(66, 76)(67, 75)(68, 74)(69, 73)(70, 72)(85, 112)(86, 111)(87, 110)(88, 109)(89, 108)(90, 107)(91, 106)(92, 105)(93, 104)(94, 103)(95, 102)(96, 101)(97, 100)(98, 99)(114, 140)(115, 139)(116, 138)(117, 137)(118, 136)(119, 135)(120, 134)(121, 133)(122, 132)(123, 131)(124, 130)(125, 129)(126, 128)(141, 168)(142, 167)(143, 166)(144, 165)(145, 164)(146, 163)(147, 162)(148, 161)(149, 160)(150, 159)(151, 158)(152, 157)(153, 156)(154, 155)
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, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168)
c: (1, 29, 59, 91, 133, 145, 15, 43, 73, 105, 119, 159)(2, 32, 68, 90, 130, 164, 16, 46, 82, 104, 116, 150)(3, 35, 77, 89, 127, 155, 17, 49, 63, 103, 113, 141)(4, 38, 58, 88, 124, 146, 18, 52, 72, 102, 138, 160)(5, 41, 67, 87, 121, 165, 19, 55, 81, 101, 135, 151)(6, 44, 76, 86, 118, 156, 20, 30, 62, 100, 132, 142)(7, 47, 57, 85, 115, 147, 21, 33, 71, 99, 129, 161)(8, 50, 66, 112, 140, 166, 22, 36, 80, 98, 126, 152)(9, 53, 75, 111, 137, 157, 23, 39, 61, 97, 123, 143)(10, 56, 84, 110, 134, 148, 24, 42, 70, 96, 120, 162)(11, 31, 65, 109, 131, 167, 25, 45, 79, 95, 117, 153)(12, 34, 74, 108, 128, 158, 26, 48, 60, 94, 114, 144)(13, 37, 83, 107, 125, 149, 27, 51, 69, 93, 139, 163)(14, 40, 64, 106, 122, 168, 28, 54, 78, 92, 136, 154)

(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[ 168, 15 ]
168
-1 56 159 29 150
-2 160 29 30 151
-3 161 30 31 152
-4 162 31 32 153
-5 33 154 163 32
-6 33 34 155 164
-7 165 34 35 156
-8 166 35 36 157
-9 167 36 37 158
-10 168 37 38 159
-11 38 39 160 141
-12 39 40 161 142
-13 143 40 41 162
-14 144 41 42 163
-15 145 42 43 164
-16 44 165 146 43
-17 44 45 166 147
-18 45 46 167 148
-19 46 47 168 149
-20 47 48 150 141
-21 48 49 151 142
-22 143 49 50 152
-23 144 50 51 153
-24 154 145 51 52
-25 155 146 52 53
-26 156 147 53 54
-27 55 157 148 54
-28 55 56 158 149
-29 1 2 59 84
-30 2 57 3 60
-31 3 58 4 61
-32 4 59 5 62
-33 5 60 6 63
-34 6 61 7 64
-35 7 62 8 65
-36 66 8 63 9
-37 67 9 64 10
-38 11 68 10 65
-39 11 66 12 69
-40 12 67 13 70
-41 13 68 14 71
-42 14 69 15 72
-43 15 70 16 73
-44 16 71 17 74
-45 17 72 18 75
-46 18 73 19 76
-47 77 19 74 20
-48 78 20 75 21
-49 22 79 21 76
-50 22 77 23 80
-51 23 78 24 81
-52 24 79 25 82
-53 25 80 26 83
-54 26 81 27 84
-55 57 27 82 28
-56 1 58 28 83
-57 55 89 30 108
-58 56 90 31 109
-59 110 91 29 32
-60 33 111 92 30
-61 34 112 93 31
-62 35 94 85 32
-63 33 36 95 86
-64 34 37 96 87
-65 88 35 38 97
-66 89 36 39 98
-67 99 90 37 40
-68 100 91 38 41
-69 101 92 39 42
-70 102 93 40 43
-71 44 103 94 41
-72 45 104 95 42
-73 46 105 96 43
-74 44 47 106 97
-75 45 48 107 98
-76 99 46 49 108
-77 100 47 50 109
-78 110 101 48 51
-79 111 102 49 52
-80 112 103 50 53
-81 104 51 85 54
-82 55 105 52 86
-83 56 106 53 87
-84 88 29 107 54
-85 81 127 62 128
-86 82 128 63 129
-87 83 129 64 130
-88 84 130 65 131
-89 66 132 57 131
-90 132 67 133 58
-91 133 68 134 59
-92 134 69 135 60
-93 135 70 136 61
-94 136 71 137 62
-95 137 72 138 63
-96 138 73 139 64
-97 139 74 140 65
-98 66 113 140 75
-99 67 113 114 76
-100 77 68 114 115
-101 78 69 115 116
-102 79 70 116 117
-103 80 71 117 118
-104 81 72 118 119
-105 82 73 119 120
-106 121 83 74 120
-107 121 122 84 75
-108 122 57 123 76
-109 77 123 58 124
-110 78 124 59 125
-111 79 125 60 126
-112 80 126 61 127
-113 99 156 98 153
-114 99 154 100 157
-115 100 155 101 158
-116 101 156 102 159
-117 102 157 103 160
-118 103 158 104 161
-119 104 159 105 162
-120 105 160 106 163
-121 106 161 107 164
-122 165 107 162 108
-123 166 108 163 109
-124 110 167 109 164
-125 110 165 111 168
-126 111 166 112 141
-127 112 167 85 142
-128 143 168 85 86
-129 144 86 141 87
-130 88 145 87 142
-131 88 143 89 146
-132 89 144 90 147
-133 90 145 91 148
-134 91 146 92 149
-135 92 147 93 150
-136 93 148 94 151
-137 94 149 95 152
-138 95 150 96 153
-139 154 96 151 97
-140 155 97 152 98
-141 11 126 129 20
-142 12 127 130 21
-143 22 13 128 131
-144 132 23 14 129
-145 133 24 15 130
-146 134 25 16 131
-147 132 135 26 17
-148 133 136 27 18
-149 134 137 28 19
-150 1 135 138 20
-151 2 136 139 21
-152 22 3 137 140
-153 23 113 4 138
-154 24 114 5 139
-155 25 115 6 140
-156 113 26 116 7
-157 114 27 117 8
-158 115 28 118 9
-159 1 116 119 10
-160 11 2 117 120
-161 121 12 3 118
-162 122 13 4 119
-163 123 14 5 120
-164 121 124 15 6
-165 122 125 16 7
-166 123 126 17 8
-167 124 127 18 9
-168 125 128 19 10
0

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