Graph forms
for C4 [ 192, 45 ] =
PL(KE_24(3,7,6,23,3),[8^12,12^8])
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On this page are computer-accessible forms for the graph C4[ 192, 45 ] =
PL(KE_24(3,7,6,23,3),[8^12,12^8]).
(I) Following is a form readable by MAGMA:
g:=Graph<192|{ {96, 105}, {96, 110}, {93, 124}, {64, 100}, {88, 124}, {77, 107},
{73, 110}, {75, 98}, {67, 104}, {81, 122}, {75, 102}, {80, 125}, {74, 100}, {66,
109}, {90, 106}, {95, 111}, {75, 122}, {90, 107}, {66, 112}, {94, 108}, {92,
111}, {80, 100}, {91, 110}, {94, 107}, {92, 105}, {72, 126}, {75, 124}, {78,
121}, {87, 111}, {64, 122}, {86, 108}, {83, 104}, {72, 117}, {83, 109}, {88,
103}, {42, 106}, {35, 98}, {39, 101}, {59, 121}, {54, 117}, {61, 126}, {39, 99},
{47, 107}, {45, 105}, {56, 124}, {56, 125}, {53, 115}, {60, 122}, {38, 109},
{48, 123}, {34, 108}, {32, 112}, {50, 98}, {62, 111}, {37, 119}, {43, 127}, {48,
100}, {63, 106}, {33, 118}, {48, 103}, {39, 127}, {54, 110}, {47, 118}, {40,
114}, {56, 98}, {60, 102}, {61, 103}, {44, 112}, {49, 108}, {59, 102}, {41,
119}, {30, 127}, {11, 104}, {18, 113}, {22, 114}, {26, 126}, {4, 97}, {21, 115},
{25, 127}, {6, 97}, {26, 125}, {13, 101}, {15, 103}, {8, 97}, {26, 115}, {10,
99}, {16, 123}, {31, 116}, {28, 119}, {15, 97}, {25, 119}, {22, 121}, {31, 112},
{29, 114}, {9, 121}, {10, 123}, {1, 115}, {3, 113}, {22, 101}, {5, 113}, {23,
99}, {15, 123}, {12, 120}, {1, 116}, {2, 116}, {19, 101}, {3, 117}, {29, 106},
{14, 118}, {30, 102}, {21, 109}, {1, 120}, {17, 104}, {2, 120}, {25, 99}, {6,
125}, {18, 105}, {9, 114}, {4, 120}, {8, 117}, {12, 113}, {1, 126}, {11, 116},
{9, 118}, {3, 131}, {30, 158}, {20, 148}, {5, 132}, {41, 168}, {18, 147}, {63,
189}, {61, 190}, {67, 192}, {36, 160}, {53, 177}, {17, 148}, {44, 169}, {42,
175}, {54, 179}, {40, 174}, {3, 132}, {36, 163}, {14, 137}, {59, 188}, {2, 138},
{24, 144}, {8, 129}, {41, 160}, {13, 132}, {51, 186}, {73, 192}, {7, 141}, {31,
149}, {24, 146}, {8, 131}, {29, 150}, {23, 156}, {9, 130}, {14, 130}, {20, 152},
{53, 185}, {21, 152}, {38, 171}, {34, 175}, {7, 137}, {36, 170}, {24, 150}, {19,
157}, {15, 129}, {58, 180}, {43, 164}, {13, 157}, {24, 136}, {27, 138}, {7,
149}, {46, 188}, {40, 186}, {36, 182}, {19, 129}, {5, 150}, {22, 133}, {50,
161}, {51, 160}, {57, 170}, {23, 131}, {26, 142}, {84, 192}, {5, 144}, {10,
156}, {33, 183}, {63, 169}, {46, 185}, {47, 183}, {20, 141}, {32, 185}, {25,
128}, {51, 170}, {28, 134}, {35, 185}, {2, 153}, {27, 128}, {16, 139}, {14,
149}, {33, 189}, {49, 173}, {58, 166}, {43, 182}, {45, 176}, {17, 143}, {57,
167}, {7, 152}, {32, 191}, {20, 139}, {11, 148}, {12, 172}, {55, 151}, {35,
130}, {39, 133}, {44, 142}, {61, 159}, {42, 137}, {21, 177}, {43, 143}, {33,
132}, {45, 136}, {37, 128}, {55, 146}, {59, 158}, {63, 154}, {49, 151}, {17,
182}, {52, 147}, {41, 129}, {50, 154}, {10, 163}, {31, 181}, {34, 137}, {40,
131}, {38, 138}, {23, 186}, {51, 158}, {52, 153}, {60, 145}, {37, 139}, {62,
144}, {54, 153}, {62, 145}, {13, 189}, {27, 171}, {37, 148}, {46, 159}, {16,
163}, {29, 174}, {19, 160}, {12, 184}, {28, 168}, {34, 151}, {46, 155}, {48,
134}, {56, 142}, {50, 133}, {53, 130}, {58, 141}, {6, 191}, {44, 149}, {35,
154}, {57, 128}, {28, 166}, {49, 139}, {30, 164}, {4, 191}, {52, 143}, {55,
140}, {60, 135}, {4, 184}, {42, 150}, {27, 167}, {58, 134}, {6, 187}, {47, 146},
{16, 173}, {11, 181}, {45, 147}, {38, 152}, {18, 172}, {52, 138}, {57, 135},
{32, 159}, {55, 136}, {71, 135}, {77, 141}, {78, 142}, {74, 140}, {91, 157},
{87, 145}, {88, 159}, {71, 143}, {76, 133}, {82, 155}, {85, 156}, {76, 135},
{80, 155}, {74, 134}, {96, 174}, {73, 153}, {79, 158}, {93, 140}, {71, 147},
{79, 154}, {71, 145}, {96, 183}, {68, 156}, {68, 157}, {73, 144}, {81, 136},
{64, 155}, {87, 140}, {74, 151}, {77, 146}, {65, 161}, {82, 178}, {83, 179},
{81, 176}, {69, 166}, {91, 184}, {86, 181}, {67, 167}, {70, 162}, {84, 176},
{64, 165}, {87, 178}, {65, 164}, {69, 163}, {76, 170}, {78, 169}, {70, 173},
{95, 180}, {94, 181}, {92, 183}, {90, 177}, {80, 187}, {85, 190}, {76, 161},
{89, 180}, {69, 171}, {70, 168}, {82, 188}, {85, 187}, {67, 172}, {94, 177},
{93, 178}, {84, 164}, {95, 175}, {86, 166}, {65, 176}, {66, 179}, {78, 188},
{79, 189}, {65, 178}, {92, 175}, {90, 169}, {69, 182}, {82, 161}, {84, 167},
{81, 165}, {89, 173}, {79, 186}, {91, 174}, {72, 190}, {77, 180}, {68, 190},
{95, 165}, {88, 162}, {72, 179}, {89, 162}, {68, 184}, {89, 165}, {66, 191},
{86, 171}, {70, 187}, {85, 168}, {62, 192}, {83, 172}, {93, 162} }>;
(II) A more general form is to represent the graph as the orbit of {96, 105}
under the group generated by the following permutations:
a: (2, 26)(3, 14)(4, 21)(5, 9)(6, 38)(7, 8)(10, 49)(11, 61)(12, 53)(13, 47)(15,
20)(17, 88)(18, 35)(19, 77)(22, 24)(23, 34)(25, 74)(27, 80)(30, 87)(31, 72)(32,
83)(36, 89)(37, 48)(39, 55)(40, 42)(41, 58)(43, 93)(44, 54)(45, 50)(46, 67)(51,
95)(52, 56)(57, 64)(59, 62)(63, 96)(68, 94)(69, 70)(71, 75)(73, 78)(76, 81)(79,
92)(82, 84)(85, 86)(90, 91)(97, 152)(98, 147)(99, 151)(100, 128)(101, 146)(102,
145)(103, 148)(104, 159)(105, 154)(106, 174)(107, 157)(108, 156)(109, 191)(110,
169)(111, 158)(112, 179)(113, 130)(114, 150)(115, 120)(116, 126)(117, 149)(118,
132)(119, 134)(121, 144)(122, 135)(123, 139)(124, 143)(125, 138)(127, 140)(129,
141)(131, 137)(133, 136)(142, 153)(155, 167)(160, 180)(161, 176)(162, 182)(163,
173)(164, 178)(165, 170)(166, 168)(171, 187)(172, 185)(175, 186)(177, 184)(181,
190)(183, 189)(188, 192) (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 **************
b: (1, 4, 8, 23, 39, 76, 60, 81, 55, 34, 7, 21)(2, 6, 3, 10, 22, 57, 75, 45, 74,
42, 20, 53)(5, 16, 9, 27, 56, 18, 48, 29, 37, 35, 52, 80)(11, 32, 54, 85, 13,
36, 59, 84, 93, 92, 58, 90)(12, 15, 40, 25, 50, 71, 64, 24, 49, 14, 38, 26)(17,
46, 73, 70, 33, 69, 78, 67, 88, 96, 28, 63)(19, 51, 30, 65, 87, 95, 77, 94, 31,
66, 72, 68)(41, 79, 43, 82, 62, 89, 47, 86, 44, 83, 61, 91)(97, 131, 99, 133,
135, 122, 136, 151, 137, 152, 115, 120)(98, 147, 100, 150, 139, 130, 138, 125,
113, 123, 114, 128)(101, 170, 102, 176, 140, 175, 141, 177, 116, 191, 117,
156)(103, 174, 119, 154, 143, 155, 144, 173, 118, 171, 142, 172)(104, 159, 110,
168, 189, 182, 188, 192, 162, 183, 166, 169)(105, 134, 106, 148, 185, 153, 187,
132, 163, 121, 167, 124)(107, 181, 112, 179, 190, 157, 160, 158, 164, 178, 111,
180)(108, 149, 109, 126, 184, 129, 186, 127, 161, 145, 165, 146)
c: (1, 2, 52, 71, 60, 75, 56, 26)(3, 5, 24, 55, 74, 48, 15, 8)(4, 54, 18, 62,
81, 93, 80, 61)(6, 72, 12, 73, 45, 87, 64, 88)(7, 20, 37, 25, 39, 22, 9, 14)(10,
19, 40, 33, 42, 77, 49, 28)(11, 27, 43, 76, 59, 35, 44, 21)(13, 29, 47, 34, 58,
16, 41, 23)(17, 57, 30, 50, 78, 53, 31, 38)(32, 66, 83, 67, 84, 65, 82, 46)(36,
51, 79, 63, 90, 94, 86, 69)(68, 91, 96, 92, 95, 89, 70, 85)(97, 117, 113, 144,
136, 140, 100, 103)(98, 142, 115, 116, 138, 143, 135, 102)(99, 101, 114, 118,
137, 141, 139, 119)(104, 167, 164, 161, 188, 185, 112, 109)(105, 111, 165, 162,
187, 190, 184, 110)(106, 107, 108, 166, 163, 160, 186, 189)(120, 153, 147, 145,
122, 124, 125, 126)(121, 130, 149, 152, 148, 128, 127, 133)(123, 129, 131, 132,
150, 146, 151, 134)(154, 169, 177, 181, 171, 182, 170, 158)(155, 159, 191, 179,
172, 192, 176, 178)(156, 157, 174, 183, 175, 180, 173, 168)
d: (2, 26)(3, 15)(4, 72)(5, 48)(6, 54)(9, 37)(10, 13)(11, 53)(12, 61)(14,
20)(16, 33)(17, 35)(18, 88)(19, 23)(21, 31)(22, 25)(24, 74)(27, 78)(28, 29)(30,
76)(32, 83)(34, 77)(36, 79)(38, 44)(40, 41)(42, 58)(43, 50)(45, 93)(46, 67)(47,
49)(52, 56)(57, 59)(62, 64)(63, 69)(70, 96)(71, 75)(73, 80)(81, 87)(82, 84)(85,
91)(86, 90)(89, 92)(97, 117)(98, 143)(99, 101)(100, 144)(102, 135)(103,
113)(104, 185)(105, 162)(106, 166)(107, 108)(109, 112)(110, 187)(111, 165)(114,
119)(115, 116)(118, 139)(120, 126)(121, 128)(122, 145)(123, 132)(124, 147)(125,
153)(127, 133)(129, 131)(130, 148)(134, 150)(136, 140)(137, 141)(138, 142)(146,
151)(149, 152)(154, 182)(155, 192)(156, 157)(158, 170)(159, 172)(160, 186)(161,
164)(163, 189)(167, 188)(168, 174)(169, 171)(173, 183)(175, 180)(176, 178)(177,
181)(179, 191)(184, 190)
e: (1, 3, 9, 26, 8, 22, 56, 15, 39, 75, 48, 25, 60, 74, 37, 71, 55, 20, 52, 24,
7, 2, 5, 14)(4, 13, 35, 61, 23, 59, 80, 41, 76, 93, 16, 43, 81, 58, 27, 62, 34,
11, 18, 47, 21, 54, 29, 44)(6, 19, 50, 88, 10, 30, 64, 28, 57, 87, 49, 17, 45,
77, 38, 73, 42, 31, 12, 33, 53, 72, 40, 78)(32, 68, 79, 46, 85, 51, 82, 70, 36,
65, 89, 69, 84, 95, 86, 67, 92, 94, 83, 96, 90, 66, 91, 63)(97, 101, 98, 103,
99, 102, 100, 119, 135, 140, 139, 143, 136, 141, 138, 144, 137, 116, 113, 118,
115, 117, 114, 142)(104, 105, 107, 109, 110, 106, 112, 184, 189, 185, 190, 186,
188, 187, 160, 161, 162, 163, 164, 165, 166, 167, 111, 108)(120, 132, 130, 126,
131, 121, 125, 129, 133, 124, 123, 127, 122, 134, 128, 145, 151, 148, 147, 146,
152, 153, 150, 149)(154, 159, 156, 158, 155, 168, 170, 178, 173, 182, 176, 180,
171, 192, 175, 181, 172, 183, 177, 179, 174, 169, 191, 157)
C4[ 192, 45 ]
192
-1 115 126 116 120
-2 116 138 120 153
-3 132 113 117 131
-4 191 184 97 120
-5 132 144 113 150
-6 187 125 191 97
-7 137 149 141 152
-8 117 129 97 131
-9 121 114 118 130
-10 99 123 156 163
-11 104 148 181 116
-12 113 172 184 120
-13 132 101 189 157
-14 137 149 118 130
-15 123 103 129 97
-16 123 139 173 163
-17 143 104 148 182
-18 113 147 105 172
-19 101 157 160 129
-20 148 139 141 152
-21 177 115 152 109
-22 121 133 101 114
-23 99 156 131 186
-24 144 146 136 150
-25 99 127 128 119
-26 125 115 126 142
-27 167 138 171 128
-28 166 134 168 119
-29 114 106 150 174
-30 102 158 127 164
-31 112 181 116 149
-32 112 191 159 185
-33 132 189 183 118
-34 137 151 108 175
-35 154 130 185 98
-36 170 160 182 163
-37 148 128 139 119
-38 138 171 152 109
-39 99 133 101 127
-40 114 174 131 186
-41 168 160 129 119
-42 137 106 150 175
-43 143 127 182 164
-44 112 169 149 142
-45 176 136 147 105
-46 155 188 159 185
-47 146 183 107 118
-48 100 123 134 103
-49 139 151 173 108
-50 154 133 161 98
-51 158 170 160 186
-52 143 147 138 153
-53 177 115 130 185
-54 110 179 117 153
-55 146 136 140 151
-56 124 125 98 142
-57 167 135 170 128
-58 166 134 180 141
-59 121 188 102 158
-60 122 145 102 135
-61 190 103 126 159
-62 111 144 145 192
-63 154 189 169 106
-64 165 100 122 155
-65 176 178 161 164
-66 112 179 191 109
-67 167 104 192 172
-68 156 157 190 184
-69 166 171 182 163
-70 187 168 162 173
-71 143 145 135 147
-72 179 190 126 117
-73 110 144 192 153
-74 100 134 140 151
-75 122 102 124 98
-76 133 135 170 161
-77 146 180 107 141
-78 121 188 169 142
-79 154 189 158 186
-80 187 100 155 125
-81 165 176 122 136
-82 155 188 178 161
-83 179 104 172 109
-84 176 167 192 164
-85 187 156 168 190
-86 166 181 171 108
-87 111 145 178 140
-88 124 103 159 162
-89 165 180 162 173
-90 177 169 106 107
-91 110 157 184 174
-92 111 105 183 175
-93 178 124 140 162
-94 177 181 107 108
-95 165 111 180 175
-96 110 105 183 174
-97 4 15 6 8
-98 56 35 50 75
-99 23 25 39 10
-100 80 48 74 64
-101 22 13 39 19
-102 59 60 30 75
-103 88 15 48 61
-104 11 67 17 83
-105 45 92 18 96
-106 90 29 63 42
-107 77 90 47 94
-108 34 49 94 86
-109 66 38 83 21
-110 91 73 96 54
-111 92 62 95 87
-112 44 66 31 32
-113 12 3 5 18
-114 22 29 40 9
-115 1 26 53 21
-116 11 1 2 31
-117 3 72 8 54
-118 33 14 47 9
-119 25 37 28 41
-120 1 12 2 4
-121 22 78 59 9
-122 81 60 64 75
-123 15 48 16 10
-124 88 56 93 75
-125 56 80 26 6
-126 1 26 61 72
-127 25 39 30 43
-128 57 25 37 27
-129 15 8 19 41
-130 35 14 9 53
-131 23 3 40 8
-132 33 13 3 5
-133 22 39 50 76
-134 58 48 28 74
-135 57 60 71 76
-136 55 45 24 81
-137 34 14 7 42
-138 2 27 38 52
-139 37 16 49 20
-140 55 93 74 87
-141 77 58 7 20
-142 44 56 78 26
-143 71 17 52 43
-144 24 5 62 73
-145 60 71 62 87
-146 55 77 24 47
-147 45 71 18 52
-148 11 37 17 20
-149 44 14 7 31
-150 24 5 29 42
-151 55 34 49 74
-152 38 7 20 21
-153 2 73 52 54
-154 35 79 50 63
-155 46 80 82 64
-156 23 68 85 10
-157 13 68 91 19
-158 79 59 51 30
-159 88 46 61 32
-160 36 51 19 41
-161 82 50 65 76
-162 88 89 70 93
-163 36 69 16 10
-164 84 30 43 65
-165 89 81 95 64
-166 58 69 28 86
-167 67 57 27 84
-168 70 28 41 85
-169 44 78 90 63
-170 57 36 51 76
-171 69 27 38 86
-172 12 67 83 18
-173 89 70 16 49
-174 91 29 40 96
-175 34 92 95 42
-176 45 81 84 65
-177 90 94 53 21
-178 82 93 65 87
-179 66 72 83 54
-180 77 89 58 95
-181 11 94 31 86
-182 36 69 17 43
-183 33 47 92 96
-184 12 68 91 4
-185 35 46 53 32
-186 23 79 40 51
-187 80 70 6 85
-188 78 46 59 82
-189 33 13 79 63
-190 68 61 72 85
-191 66 4 6 32
-192 67 62 73 84
0