Graph forms
for C4 [ 234, 9 ] = PS(6,39;14)
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On this page are computer-accessible forms for the graph C4[ 234, 9 ] =
PS(6,39;14).
(I) Following is a form readable by MAGMA:
g:=Graph<234|{ {117, 118}, {195, 196}, {65, 79}, {144, 158}, {145, 159}, {39,
40}, {66, 80}, {78, 92}, {75, 89}, {74, 88}, {71, 85}, {70, 84}, {67, 81}, {143,
157}, {68, 82}, {77, 91}, {76, 90}, {69, 83}, {64, 89}, {70, 95}, {68, 93}, {66,
91}, {132, 157}, {134, 159}, {65, 90}, {69, 94}, {133, 158}, {72, 86}, {73, 87},
{67, 92}, {8, 46}, {193, 231}, {192, 230}, {81, 119}, {80, 118}, {9, 47}, {16,
54}, {17, 55}, {24, 62}, {25, 63}, {88, 126}, {89, 127}, {71, 96}, {135, 160},
{143, 168}, {151, 176}, {1, 41}, {194, 234}, {193, 233}, {192, 232}, {83, 123},
{82, 122}, {81, 121}, {80, 120}, {2, 42}, {3, 43}, {4, 44}, {5, 45}, {6, 46},
{7, 47}, {16, 56}, {17, 57}, {18, 58}, {19, 59}, {20, 60}, {21, 61}, {22, 62},
{23, 63}, {84, 124}, {85, 125}, {86, 126}, {87, 127}, {72, 97}, {78, 103}, {76,
101}, {74, 99}, {136, 161}, {138, 163}, {140, 165}, {142, 167}, {152, 177},
{154, 179}, {156, 181}, {2, 40}, {195, 233}, {194, 232}, {83, 121}, {82, 120},
{3, 41}, {6, 44}, {7, 45}, {18, 56}, {19, 57}, {22, 60}, {23, 61}, {86, 124},
{87, 125}, {73, 98}, {77, 102}, {137, 162}, {141, 166}, {153, 178}, {4, 42},
{84, 122}, {5, 43}, {20, 58}, {21, 59}, {85, 123}, {75, 100}, {139, 164}, {155,
180}, {146, 160}, {147, 161}, {150, 164}, {151, 165}, {154, 168}, {155, 169},
{64, 117}, {128, 181}, {130, 183}, {136, 189}, {138, 191}, {148, 162}, {149,
163}, {156, 170}, {129, 182}, {137, 190}, {8, 48}, {79, 119}, {9, 49}, {10, 50},
{11, 51}, {12, 52}, {13, 53}, {14, 54}, {15, 55}, {144, 169}, {146, 171}, {148,
173}, {150, 175}, {10, 48}, {11, 49}, {14, 52}, {15, 53}, {131, 184}, {135,
188}, {145, 170}, {149, 174}, {132, 185}, {134, 187}, {12, 50}, {13, 51}, {152,
166}, {153, 167}, {133, 186}, {147, 172}, {40, 104}, {53, 117}, {52, 116}, {51,
115}, {50, 114}, {49, 113}, {48, 112}, {47, 111}, {46, 110}, {45, 109}, {44,
108}, {43, 107}, {42, 106}, {41, 105}, {128, 192}, {129, 193}, {130, 194}, {131,
195}, {43, 96}, {63, 116}, {59, 112}, {47, 100}, {139, 192}, {44, 97}, {62,
115}, {60, 113}, {46, 99}, {140, 193}, {142, 195}, {1, 78}, {61, 114}, {45, 98},
{141, 194}, {48, 101}, {58, 111}, {56, 109}, {50, 103}, {49, 102}, {57, 110},
{24, 64}, {191, 231}, {190, 230}, {189, 229}, {188, 228}, {187, 227}, {186,
226}, {185, 225}, {184, 224}, {159, 199}, {158, 198}, {25, 65}, {26, 66}, {27,
67}, {28, 68}, {29, 69}, {30, 70}, {31, 71}, {157, 197}, {26, 64}, {191, 229},
{190, 228}, {187, 225}, {186, 224}, {159, 197}, {27, 65}, {30, 68}, {31, 69},
{158, 196}, {51, 104}, {55, 108}, {52, 105}, {54, 107}, {28, 66}, {189, 227},
{188, 226}, {29, 67}, {53, 106}, {32, 70}, {185, 223}, {184, 222}, {177, 215},
{176, 214}, {169, 207}, {168, 206}, {161, 199}, {160, 198}, {33, 71}, {55, 80},
{63, 88}, {32, 72}, {183, 223}, {182, 222}, {181, 221}, {180, 220}, {179, 219},
{178, 218}, {177, 217}, {176, 216}, {167, 207}, {166, 206}, {165, 205}, {164,
204}, {163, 203}, {162, 202}, {161, 201}, {160, 200}, {38, 78}, {37, 77}, {36,
76}, {35, 75}, {33, 73}, {34, 74}, {56, 81}, {62, 87}, {60, 85}, {58, 83}, {34,
72}, {183, 221}, {182, 220}, {179, 217}, {178, 216}, {167, 205}, {166, 204},
{163, 201}, {162, 200}, {39, 77}, {38, 76}, {35, 73}, {57, 82}, {61, 86}, {36,
74}, {181, 219}, {180, 218}, {165, 203}, {164, 202}, {37, 75}, {59, 84}, {40,
93}, {42, 95}, {41, 94}, {157, 234}, {168, 208}, {175, 215}, {174, 214}, {173,
213}, {172, 212}, {171, 211}, {170, 210}, {169, 209}, {54, 79}, {170, 208},
{175, 213}, {174, 212}, {171, 209}, {172, 210}, {173, 211}, {118, 182}, {119,
183}, {120, 184}, {121, 185}, {122, 186}, {123, 187}, {124, 188}, {125, 189},
{126, 190}, {127, 191}, {15, 196}, {27, 208}, {31, 212}, {123, 176}, {127, 180},
{28, 209}, {30, 211}, {124, 177}, {126, 179}, {29, 210}, {125, 178}, {2, 211},
{4, 213}, {6, 215}, {8, 217}, {10, 219}, {12, 221}, {14, 223}, {1, 210}, {79,
156}, {5, 214}, {9, 218}, {13, 222}, {16, 197}, {18, 199}, {24, 205}, {26, 207},
{120, 173}, {122, 175}, {30, 200}, {31, 201}, {3, 212}, {11, 220}, {17, 198},
{25, 206}, {121, 174}, {88, 128}, {89, 129}, {90, 130}, {91, 131}, {92, 132},
{93, 133}, {94, 134}, {95, 135}, {28, 198}, {29, 199}, {90, 128}, {91, 129},
{94, 132}, {95, 133}, {19, 200}, {23, 204}, {119, 172}, {1, 221}, {2, 222}, {3,
223}, {20, 201}, {22, 203}, {118, 171}, {26, 196}, {27, 197}, {92, 130}, {93,
131}, {7, 216}, {21, 202}, {4, 224}, {5, 225}, {6, 226}, {7, 227}, {12, 232},
{13, 233}, {14, 234}, {96, 134}, {97, 135}, {104, 142}, {105, 143}, {112, 150},
{113, 151}, {96, 136}, {97, 137}, {98, 138}, {99, 139}, {100, 140}, {101, 141},
{102, 142}, {103, 143}, {112, 152}, {113, 153}, {114, 154}, {115, 155}, {116,
156}, {32, 202}, {37, 207}, {36, 206}, {33, 203}, {98, 136}, {99, 137}, {102,
140}, {103, 141}, {114, 152}, {115, 153}, {8, 228}, {9, 229}, {10, 230}, {11,
231}, {34, 204}, {35, 205}, {100, 138}, {101, 139}, {116, 154}, {117, 155}, {15,
224}, {16, 225}, {18, 227}, {20, 229}, {22, 231}, {24, 233}, {17, 226}, {21,
230}, {25, 234}, {32, 213}, {34, 215}, {38, 208}, {39, 209}, {19, 228}, {33,
214}, {104, 144}, {105, 145}, {106, 146}, {107, 147}, {108, 148}, {109, 149},
{110, 150}, {111, 151}, {106, 144}, {107, 145}, {110, 148}, {111, 149}, {35,
216}, {39, 220}, {36, 217}, {38, 219}, {108, 146}, {109, 147}, {23, 232}, {37,
218} }>;
(II) A more general form is to represent the graph as the orbit of {117, 118}
under the group generated by the following permutations:
a: (1, 40)(2, 41)(3, 42)(4, 43)(5, 44)(6, 45)(7, 46)(8, 47)(9, 48)(10, 49)(11,
50)(12, 51)(13, 52)(14, 53)(15, 54)(16, 55)(17, 56)(18, 57)(19, 58)(20, 59)(21,
60)(22, 61)(23, 62)(24, 63)(25, 64)(26, 65)(27, 66)(28, 67)(29, 68)(30, 69)(31,
70)(32, 71)(33, 72)(34, 73)(35, 74)(36, 75)(37, 76)(38, 77)(39, 78)(79, 196)(80,
197)(81, 198)(82, 199)(83, 200)(84, 201)(85, 202)(86, 203)(87, 204)(88, 205)(89,
206)(90, 207)(91, 208)(92, 209)(93, 210)(94, 211)(95, 212)(96, 213)(97, 214)(98,
215)(99, 216)(100, 217)(101, 218)(102, 219)(103, 220)(104, 221)(105, 222)(106,
223)(107, 224)(108, 225)(109, 226)(110, 227)(111, 228)(112, 229)(113, 230)(114,
231)(115, 232)(116, 233)(117, 234)(118, 157)(119, 158)(120, 159)(121, 160)(122,
161)(123, 162)(124, 163)(125, 164)(126, 165)(127, 166)(128, 167)(129, 168)(130,
169)(131, 170)(132, 171)(133, 172)(134, 173)(135, 174)(136, 175)(137, 176)(138,
177)(139, 178)(140, 179)(141, 180)(142, 181)(143, 182)(144, 183)(145, 184)(146,
185)(147, 186)(148, 187)(149, 188)(150, 189)(151, 190)(152, 191)(153, 192)(154,
193)(155, 194)(156, 195) (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: (2, 15)(3, 29)(5, 18)(6, 32)(8, 21)(9, 35)(11, 24)(12, 38)(14, 27)(17,
30)(20, 33)(23, 36)(26, 39)(40, 196)(41, 210)(42, 224)(43, 199)(44, 213)(45,
227)(46, 202)(47, 216)(48, 230)(49, 205)(50, 219)(51, 233)(52, 208)(53, 222)(54,
197)(55, 211)(56, 225)(57, 200)(58, 214)(59, 228)(60, 203)(61, 217)(62, 231)(63,
206)(64, 220)(65, 234)(66, 209)(67, 223)(68, 198)(69, 212)(70, 226)(71, 201)(72,
215)(73, 229)(74, 204)(75, 218)(76, 232)(77, 207)(78, 221)(79, 157)(80, 171)(81,
185)(82, 160)(83, 174)(84, 188)(85, 163)(86, 177)(87, 191)(88, 166)(89, 180)(90,
194)(91, 169)(92, 183)(93, 158)(94, 172)(95, 186)(96, 161)(97, 175)(98, 189)(99,
164)(100, 178)(101, 192)(102, 167)(103, 181)(104, 195)(105, 170)(106, 184)(107,
159)(108, 173)(109, 187)(110, 162)(111, 176)(112, 190)(113, 165)(114, 179)(115,
193)(116, 168)(117, 182)(119, 132)(120, 146)(122, 135)(123, 149)(125, 138)(126,
152)(128, 141)(129, 155)(131, 144)(134, 147)(137, 150)(140, 153)(143, 156)
c: (2, 26)(3, 12)(4, 37)(5, 23)(6, 9)(7, 34)(8, 20)(10, 31)(11, 17)(13, 28)(15,
39)(16, 25)(18, 36)(19, 22)(21, 33)(24, 30)(29, 38)(32, 35)(40, 196)(41,
221)(42, 207)(43, 232)(44, 218)(45, 204)(46, 229)(47, 215)(48, 201)(49, 226)(50,
212)(51, 198)(52, 223)(53, 209)(54, 234)(55, 220)(56, 206)(57, 231)(58, 217)(59,
203)(60, 228)(61, 214)(62, 200)(63, 225)(64, 211)(65, 197)(66, 222)(67, 208)(68,
233)(69, 219)(70, 205)(71, 230)(72, 216)(73, 202)(74, 227)(75, 213)(76, 199)(77,
224)(78, 210)(79, 157)(80, 182)(81, 168)(82, 193)(83, 179)(84, 165)(85, 190)(86,
176)(87, 162)(88, 187)(89, 173)(90, 159)(91, 184)(92, 170)(93, 195)(94, 181)(95,
167)(96, 192)(97, 178)(98, 164)(99, 189)(100, 175)(101, 161)(102, 186)(103,
172)(104, 158)(105, 183)(106, 169)(107, 194)(108, 180)(109, 166)(110, 191)(111,
177)(112, 163)(113, 188)(114, 174)(115, 160)(116, 185)(117, 171)(119, 143)(120,
129)(121, 154)(122, 140)(123, 126)(124, 151)(125, 137)(127, 148)(128, 134)(130,
145)(132, 156)(133, 142)(135, 153)(136, 139)(138, 150)(141, 147)(146, 155)(149,
152)
d: (2, 91, 15, 169)(3, 181, 29, 103)(4, 37)(5, 88, 18, 166)(6, 178, 32, 100)(7,
34)(8, 85, 21, 163)(9, 175, 35, 97)(10, 31)(11, 82, 24, 160)(12, 172, 38,
94)(13, 28)(14, 79, 27, 157)(16, 25)(17, 115, 30, 193)(19, 22)(20, 112, 33,
190)(23, 109, 36, 187)(26, 106, 39, 184)(40, 131, 196, 144)(41, 221, 210,
78)(42, 77, 224, 207)(43, 128, 199, 141)(44, 218, 213, 75)(45, 74, 227, 204)(46,
125, 202, 138)(47, 215, 216, 72)(48, 71, 230, 201)(49, 122, 205, 135)(50, 212,
219, 69)(51, 68, 233, 198)(52, 119, 208, 132)(53, 209, 222, 66)(54, 65, 197,
234)(55, 155, 211, 129)(56, 206, 225, 63)(57, 62, 200, 231)(58, 152, 214,
126)(59, 203, 228, 60)(61, 149, 217, 123)(64, 146, 220, 120)(67, 143, 223,
156)(70, 140, 226, 153)(73, 137, 229, 150)(76, 134, 232, 147)(80, 117, 171,
182)(81, 168, 185, 116)(83, 114, 174, 179)(84, 165, 188, 113)(86, 111, 177,
176)(87, 162, 191, 110)(89, 108, 180, 173)(90, 159, 194, 107)(92, 105, 183,
170)(93, 195, 158, 104)(95, 102, 186, 167)(96, 192, 161, 101)(98, 99, 189,
164)(121, 154)(124, 151)(127, 148)(130, 145)(133, 142)(136, 139)
e: (1, 2)(3, 39)(4, 38)(5, 37)(6, 36)(7, 35)(8, 34)(9, 33)(10, 32)(11, 31)(12,
30)(13, 29)(14, 28)(15, 27)(16, 26)(17, 25)(18, 24)(19, 23)(20, 22)(40, 41)(42,
78)(43, 77)(44, 76)(45, 75)(46, 74)(47, 73)(48, 72)(49, 71)(50, 70)(51, 69)(52,
68)(53, 67)(54, 66)(55, 65)(56, 64)(57, 63)(58, 62)(59, 61)(79, 80)(81, 117)(82,
116)(83, 115)(84, 114)(85, 113)(86, 112)(87, 111)(88, 110)(89, 109)(90, 108)(91,
107)(92, 106)(93, 105)(94, 104)(95, 103)(96, 102)(97, 101)(98, 100)(118,
119)(120, 156)(121, 155)(122, 154)(123, 153)(124, 152)(125, 151)(126, 150)(127,
149)(128, 148)(129, 147)(130, 146)(131, 145)(132, 144)(133, 143)(134, 142)(135,
141)(136, 140)(137, 139)(157, 158)(159, 195)(160, 194)(161, 193)(162, 192)(163,
191)(164, 190)(165, 189)(166, 188)(167, 187)(168, 186)(169, 185)(170, 184)(171,
183)(172, 182)(173, 181)(174, 180)(175, 179)(176, 178)(196, 197)(198, 234)(199,
233)(200, 232)(201, 231)(202, 230)(203, 229)(204, 228)(205, 227)(206, 226)(207,
225)(208, 224)(209, 223)(210, 222)(211, 221)(212, 220)(213, 219)(214, 218)(215,
217)
C4[ 234, 9 ]
234
-1 78 210 221 41
-2 211 222 40 42
-3 212 223 41 43
-4 44 213 224 42
-5 45 214 225 43
-6 44 46 215 226
-7 45 47 216 227
-8 46 48 217 228
-9 47 49 218 229
-10 48 50 219 230
-11 220 231 49 51
-12 221 232 50 52
-13 222 233 51 53
-14 223 234 52 54
-15 55 224 53 196
-16 56 225 54 197
-17 55 198 57 226
-18 56 199 58 227
-19 57 200 59 228
-20 58 201 60 229
-21 59 202 61 230
-22 231 60 203 62
-23 232 61 204 63
-24 233 62 205 64
-25 234 63 206 65
-26 66 64 196 207
-27 67 65 197 208
-28 66 198 209 68
-29 67 199 210 69
-30 68 200 211 70
-31 69 201 212 71
-32 70 202 213 72
-33 71 203 214 73
-34 72 204 215 74
-35 73 205 216 75
-36 74 206 217 76
-37 77 75 207 218
-38 78 76 208 219
-39 77 209 220 40
-40 2 93 104 39
-41 1 3 94 105
-42 2 4 95 106
-43 3 5 96 107
-44 4 6 97 108
-45 5 7 98 109
-46 99 110 6 8
-47 100 111 7 9
-48 101 112 8 10
-49 11 102 113 9
-50 12 103 114 10
-51 11 13 104 115
-52 12 14 105 116
-53 13 15 106 117
-54 79 14 16 107
-55 80 15 17 108
-56 81 16 18 109
-57 110 82 17 19
-58 111 83 18 20
-59 112 84 19 21
-60 22 113 85 20
-61 23 114 86 21
-62 22 24 115 87
-63 88 23 25 116
-64 89 24 26 117
-65 79 90 25 27
-66 80 91 26 28
-67 81 92 27 29
-68 82 93 28 30
-69 83 94 29 31
-70 84 95 30 32
-71 33 85 96 31
-72 34 86 97 32
-73 33 35 87 98
-74 88 99 34 36
-75 89 100 35 37
-76 90 101 36 38
-77 91 102 37 39
-78 1 92 103 38
-79 156 119 54 65
-80 55 66 118 120
-81 121 56 67 119
-82 122 57 68 120
-83 121 123 58 69
-84 122 124 59 70
-85 123 125 60 71
-86 124 126 61 72
-87 125 127 62 73
-88 126 128 63 74
-89 127 129 64 75
-90 128 130 65 76
-91 66 77 129 131
-92 132 67 78 130
-93 133 68 40 131
-94 132 134 69 41
-95 133 135 70 42
-96 134 136 71 43
-97 44 135 137 72
-98 45 136 138 73
-99 46 137 139 74
-100 47 138 140 75
-101 48 139 141 76
-102 77 49 140 142
-103 143 78 50 141
-104 144 40 51 142
-105 143 145 41 52
-106 144 146 42 53
-107 145 147 43 54
-108 44 55 146 148
-109 45 56 147 149
-110 46 57 148 150
-111 47 58 149 151
-112 48 59 150 152
-113 49 60 151 153
-114 154 50 61 152
-115 155 51 62 153
-116 154 156 52 63
-117 155 118 53 64
-118 80 171 182 117
-119 79 81 172 183
-120 80 82 173 184
-121 81 83 174 185
-122 82 84 175 186
-123 176 187 83 85
-124 177 188 84 86
-125 178 189 85 87
-126 88 179 190 86
-127 89 180 191 87
-128 88 90 181 192
-129 89 91 182 193
-130 90 92 183 194
-131 91 93 184 195
-132 157 92 94 185
-133 158 93 95 186
-134 187 159 94 96
-135 188 160 95 97
-136 189 161 96 98
-137 99 190 162 97
-138 100 191 163 98
-139 99 101 192 164
-140 165 100 102 193
-141 166 101 103 194
-142 167 102 104 195
-143 157 168 103 105
-144 158 169 104 106
-145 159 170 105 107
-146 160 171 106 108
-147 161 172 107 109
-148 110 162 173 108
-149 111 163 174 109
-150 110 112 164 175
-151 165 176 111 113
-152 166 177 112 114
-153 167 178 113 115
-154 168 179 114 116
-155 169 180 115 117
-156 79 170 181 116
-157 132 143 234 197
-158 198 133 144 196
-159 199 134 145 197
-160 198 200 135 146
-161 199 201 136 147
-162 200 202 137 148
-163 201 203 138 149
-164 202 204 139 150
-165 203 205 140 151
-166 204 206 141 152
-167 205 207 142 153
-168 143 154 206 208
-169 209 144 155 207
-170 210 145 156 208
-171 209 211 146 118
-172 210 212 147 119
-173 211 213 148 120
-174 121 212 214 149
-175 122 213 215 150
-176 123 214 216 151
-177 124 215 217 152
-178 125 216 218 153
-179 154 126 217 219
-180 220 155 127 218
-181 221 156 128 219
-182 220 222 118 129
-183 221 223 119 130
-184 222 224 120 131
-185 121 132 223 225
-186 122 133 224 226
-187 123 134 225 227
-188 124 135 226 228
-189 125 136 227 229
-190 126 137 228 230
-191 231 127 138 229
-192 232 128 139 230
-193 231 233 129 140
-194 232 234 130 141
-195 233 196 131 142
-196 15 26 158 195
-197 157 16 27 159
-198 158 17 28 160
-199 159 18 29 161
-200 160 19 30 162
-201 161 20 31 163
-202 162 21 32 164
-203 22 33 165 163
-204 23 34 166 164
-205 165 24 35 167
-206 166 25 36 168
-207 167 26 37 169
-208 168 27 38 170
-209 169 28 39 171
-210 1 170 29 172
-211 2 171 30 173
-212 3 172 31 174
-213 4 173 32 175
-214 33 176 5 174
-215 34 177 6 175
-216 176 35 178 7
-217 177 36 179 8
-218 178 37 180 9
-219 179 38 181 10
-220 11 180 39 182
-221 1 12 181 183
-222 2 13 182 184
-223 3 14 183 185
-224 4 15 184 186
-225 187 5 16 185
-226 188 6 17 186
-227 187 189 7 18
-228 188 190 8 19
-229 189 191 9 20
-230 190 192 10 21
-231 11 22 191 193
-232 12 23 192 194
-233 13 24 193 195
-234 14 25 157 194
0