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On this page are computer-accessible forms for the graph C4[ 162, 5 ] = PS(6,27;8).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {108, 109} under the group generated by the following permutations:

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

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

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