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On this page are computer-accessible forms for the graph C4[ 165, 5 ] = PS(15,11;3).

(I) Following is a form readable by MAGMA:

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

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

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

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