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On this page are computer-accessible forms for the graph C4[ 165, 4 ] = PS(15,11;2).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {66, 67} under the group generated by the following permutations:

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

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

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