[Home] [Table] [Glossary] [Families]

On this page are computer-accessible forms for the graph C4[ 168, 10 ] = PS(14,24;5).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {24, 27} under the group generated by the following permutations:

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

(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.

**************

&Graph
C4[ 168, 10 ]
168
-1 166 13 24 159
-2 13 167 14 160
-3 14 168 15 161
-4 157 15 16 162
-5 158 16 17 163
-6 159 17 18 164
-7 165 160 18 19
-8 166 161 19 20
-9 167 162 20 21
-10 22 168 163 21
-11 22 23 157 164
-12 165 23 24 158
-13 1 2 35 28
-14 2 3 36 29
-15 3 25 4 30
-16 4 26 5 31
-17 5 27 6 32
-18 33 6 28 7
-19 34 7 29 8
-20 35 8 30 9
-21 36 9 31 10
-22 11 25 10 32
-23 11 33 12 26
-24 1 12 34 27
-25 22 15 37 48
-26 23 37 16 38
-27 24 38 17 39
-28 13 39 18 40
-29 14 40 19 41
-30 15 41 20 42
-31 16 42 21 43
-32 22 44 17 43
-33 44 23 45 18
-34 45 24 46 19
-35 13 46 47 20
-36 14 47 48 21
-37 25 26 59 52
-38 26 27 60 53
-39 27 49 28 54
-40 55 28 50 29
-41 56 29 51 30
-42 57 30 52 31
-43 58 31 53 32
-44 33 59 32 54
-45 33 55 34 60
-46 34 56 35 49
-47 35 57 36 50
-48 25 36 58 51
-49 46 39 61 72
-50 47 61 40 62
-51 48 62 41 63
-52 37 63 42 64
-53 38 64 43 65
-54 44 66 39 65
-55 66 45 67 40
-56 67 46 68 41
-57 68 47 69 42
-58 69 48 70 43
-59 44 37 70 71
-60 45 38 71 72
-61 49 50 83 76
-62 77 50 51 84
-63 78 51 73 52
-64 79 52 74 53
-65 80 53 75 54
-66 55 81 54 76
-67 55 77 56 82
-68 56 78 57 83
-69 57 79 58 84
-70 58 80 59 73
-71 59 81 60 74
-72 49 60 82 75
-73 70 63 85 96
-74 71 85 64 86
-75 72 86 65 87
-76 66 88 61 87
-77 88 67 89 62
-78 89 68 90 63
-79 90 69 91 64
-80 91 70 92 65
-81 66 92 71 93
-82 67 93 72 94
-83 68 61 94 95
-84 69 62 95 96
-85 100 73 74 107
-86 101 74 75 108
-87 102 75 97 76
-88 77 103 76 98
-89 77 99 78 104
-90 78 100 79 105
-91 79 101 80 106
-92 80 102 81 107
-93 81 103 82 108
-94 82 104 83 97
-95 83 105 84 98
-96 99 73 84 106
-97 94 87 109 120
-98 88 110 95 109
-99 110 89 111 96
-100 111 90 112 85
-101 112 91 113 86
-102 113 92 114 87
-103 88 114 93 115
-104 89 115 94 116
-105 90 116 95 117
-106 91 117 96 118
-107 92 85 118 119
-108 93 86 119 120
-109 124 97 98 131
-110 99 132 125 98
-111 99 121 100 126
-112 100 122 101 127
-113 101 123 102 128
-114 102 124 103 129
-115 103 125 104 130
-116 104 126 105 131
-117 132 105 127 106
-118 121 106 128 107
-119 122 107 129 108
-120 123 97 108 130
-121 111 133 144 118
-122 133 112 134 119
-123 134 113 135 120
-124 135 114 136 109
-125 110 136 115 137
-126 111 137 116 138
-127 112 138 117 139
-128 113 139 118 140
-129 114 140 119 141
-130 115 141 120 142
-131 143 116 109 142
-132 110 143 144 117
-133 121 122 155 148
-134 122 123 156 149
-135 123 145 124 150
-136 124 146 125 151
-137 125 147 126 152
-138 126 148 127 153
-139 154 127 149 128
-140 155 128 150 129
-141 156 129 151 130
-142 145 130 152 131
-143 132 146 131 153
-144 121 132 154 147
-145 135 157 168 142
-146 143 157 136 158
-147 144 158 137 159
-148 133 159 138 160
-149 134 160 139 161
-150 135 161 140 162
-151 136 162 141 163
-152 137 163 142 164
-153 143 165 138 164
-154 165 144 166 139
-155 133 166 167 140
-156 134 167 168 141
-157 11 145 146 4
-158 12 146 147 5
-159 1 147 148 6
-160 2 148 149 7
-161 3 149 150 8
-162 4 150 151 9
-163 5 151 152 10
-164 11 6 152 153
-165 154 12 7 153
-166 154 1 155 8
-167 155 2 156 9
-168 145 156 3 10
0

**************