C4graphGraph forms for C4 [ 240, 56 ] = KE_60(1,31,13,27,16)

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On this page are computer-accessible forms for the graph C4[ 240, 56 ] = KE_60(1,31,13,27,16).

(I) Following is a form readable by MAGMA:

g:=Graph<240|{ {2, 3}, {58, 59}, {56, 57}, {54, 55}, {52, 53}, {50, 51}, {48, 49}, {46, 47}, {44, 45}, {42, 43}, {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}, {1, 2}, {57, 58}, {53, 54}, {49, 50}, {45, 46}, {5, 6}, {9, 10}, {13, 14}, {17, 18}, {21, 22}, {25, 26}, {29, 30}, {33, 34}, {37, 38}, {41, 42}, {3, 4}, {59, 60}, {51, 52}, {43, 44}, {11, 12}, {19, 20}, {27, 28}, {35, 36}, {112, 125}, {114, 127}, {7, 8}, {55, 56}, {23, 24}, {39, 40}, {113, 126}, {192, 208}, {224, 240}, {207, 223}, {206, 222}, {205, 221}, {204, 220}, {203, 219}, {202, 218}, {201, 217}, {200, 216}, {199, 215}, {198, 214}, {197, 213}, {196, 212}, {195, 211}, {194, 210}, {193, 209}, {111, 124}, {108, 121}, {110, 123}, {109, 122}, {32, 61}, {34, 63}, {15, 16}, {47, 48}, {33, 62}, {192, 236}, {195, 239}, {194, 238}, {193, 237}, {208, 224}, {223, 239}, {222, 238}, {221, 237}, {220, 236}, {219, 235}, {218, 234}, {217, 233}, {216, 232}, {215, 231}, {214, 230}, {213, 229}, {212, 228}, {211, 227}, {210, 226}, {209, 225}, {196, 240}, {64, 124}, {67, 127}, {66, 126}, {65, 125}, {128, 188}, {129, 189}, {130, 190}, {131, 191}, {1, 60}, {31, 32}, {61, 121}, {180, 240}, {175, 235}, {174, 234}, {173, 233}, {172, 232}, {167, 227}, {166, 226}, {165, 225}, {164, 224}, {159, 219}, {158, 218}, {157, 217}, {156, 216}, {151, 211}, {150, 210}, {149, 209}, {148, 208}, {143, 203}, {142, 202}, {141, 201}, {140, 200}, {63, 123}, {62, 122}, {132, 192}, {133, 193}, {134, 194}, {135, 195}, {136, 196}, {171, 231}, {170, 230}, {169, 229}, {168, 228}, {155, 215}, {154, 214}, {153, 213}, {152, 212}, {137, 197}, {138, 198}, {139, 199}, {181, 225}, {191, 235}, {190, 234}, {189, 233}, {188, 232}, {183, 227}, {182, 226}, {2, 91}, {4, 93}, {6, 95}, {1, 90}, {5, 94}, {144, 204}, {187, 231}, {186, 230}, {185, 229}, {184, 228}, {179, 239}, {178, 238}, {177, 237}, {176, 236}, {147, 207}, {146, 206}, {145, 205}, {3, 92}, {35, 64}, {59, 88}, {55, 84}, {51, 80}, {47, 76}, {43, 72}, {39, 68}, {36, 65}, {60, 89}, {54, 83}, {52, 81}, {46, 75}, {44, 73}, {38, 67}, {7, 96}, {53, 82}, {45, 74}, {15, 104}, {23, 112}, {31, 120}, {37, 66}, {8, 97}, {10, 99}, {12, 101}, {14, 103}, {24, 113}, {26, 115}, {28, 117}, {30, 119}, {9, 98}, {13, 102}, {25, 114}, {29, 118}, {40, 69}, {58, 87}, {56, 85}, {42, 71}, {11, 100}, {57, 86}, {27, 116}, {41, 70}, {181, 197}, {191, 207}, {190, 206}, {189, 205}, {188, 204}, {187, 203}, {186, 202}, {185, 201}, {184, 200}, {183, 199}, {182, 198}, {1, 121}, {2, 122}, {3, 123}, {4, 124}, {5, 125}, {6, 126}, {7, 127}, {16, 105}, {18, 107}, {20, 109}, {22, 111}, {17, 106}, {21, 110}, {160, 220}, {163, 223}, {162, 222}, {161, 221}, {48, 77}, {50, 79}, {19, 108}, {49, 78}, {8, 128}, {60, 180}, {59, 179}, {58, 178}, {57, 177}, {56, 176}, {47, 167}, {46, 166}, {45, 165}, {44, 164}, {43, 163}, {42, 162}, {41, 161}, {9, 129}, {10, 130}, {11, 131}, {12, 132}, {13, 133}, {14, 134}, {15, 135}, {24, 144}, {25, 145}, {26, 146}, {27, 147}, {28, 148}, {29, 149}, {30, 150}, {31, 151}, {40, 160}, {64, 211}, {72, 219}, {68, 215}, {76, 223}, {65, 212}, {73, 220}, {67, 214}, {75, 222}, {66, 213}, {74, 221}, {16, 136}, {55, 175}, {54, 174}, {53, 173}, {52, 172}, {51, 171}, {50, 170}, {49, 169}, {48, 168}, {17, 137}, {18, 138}, {19, 139}, {20, 140}, {21, 141}, {22, 142}, {23, 143}, {69, 216}, {71, 218}, {70, 217}, {105, 192}, {107, 194}, {109, 196}, {111, 198}, {106, 193}, {110, 197}, {77, 224}, {79, 226}, {93, 240}, {78, 225}, {108, 195}, {80, 227}, {84, 231}, {88, 235}, {92, 239}, {81, 228}, {83, 230}, {89, 236}, {91, 238}, {63, 136}, {82, 229}, {90, 237}, {112, 199}, {120, 207}, {32, 152}, {33, 153}, {34, 154}, {35, 155}, {36, 156}, {37, 157}, {38, 158}, {39, 159}, {62, 135}, {113, 200}, {115, 202}, {117, 204}, {119, 206}, {61, 134}, {114, 201}, {118, 205}, {85, 232}, {87, 234}, {86, 233}, {116, 203}, {68, 128}, {71, 131}, {70, 130}, {69, 129}, {76, 136}, {77, 137}, {78, 138}, {79, 139}, {84, 144}, {85, 145}, {86, 146}, {87, 147}, {92, 152}, {93, 153}, {94, 154}, {95, 155}, {100, 160}, {101, 161}, {102, 162}, {103, 163}, {108, 168}, {109, 169}, {110, 170}, {111, 171}, {116, 176}, {117, 177}, {118, 178}, {119, 179}, {124, 184}, {125, 185}, {126, 186}, {127, 187}, {64, 137}, {70, 143}, {68, 141}, {66, 139}, {80, 153}, {82, 155}, {84, 157}, {86, 159}, {96, 169}, {98, 171}, {100, 173}, {102, 175}, {65, 138}, {69, 142}, {81, 154}, {85, 158}, {97, 170}, {101, 174}, {72, 132}, {74, 134}, {73, 133}, {75, 135}, {88, 148}, {89, 149}, {90, 150}, {91, 151}, {104, 164}, {105, 165}, {106, 166}, {107, 167}, {120, 180}, {121, 181}, {122, 182}, {123, 183}, {67, 140}, {83, 156}, {99, 172}, {71, 144}, {79, 152}, {96, 183}, {103, 176}, {104, 191}, {72, 145}, {74, 147}, {76, 149}, {78, 151}, {97, 184}, {99, 186}, {101, 188}, {103, 190}, {104, 177}, {106, 179}, {73, 146}, {77, 150}, {98, 185}, {102, 189}, {105, 178}, {80, 140}, {81, 141}, {82, 142}, {83, 143}, {112, 172}, {113, 173}, {114, 174}, {115, 175}, {75, 148}, {100, 187}, {107, 180}, {95, 182}, {94, 181}, {61, 208}, {63, 210}, {62, 209}, {115, 128}, {119, 132}, {116, 129}, {118, 131}, {87, 160}, {95, 168}, {117, 130}, {88, 161}, {90, 163}, {92, 165}, {94, 167}, {89, 162}, {93, 166}, {96, 156}, {97, 157}, {98, 158}, {99, 159}, {120, 133}, {91, 164} }>;

(II) A more general form is to represent the graph as the orbit of {2, 3} under the group generated by the following permutations:

a: (2, 60)(3, 59)(4, 58)(5, 57)(6, 56)(7, 55)(8, 54)(9, 53)(10, 52)(11, 51)(12, 50)(13, 49)(14, 48)(15, 47)(16, 46)(17, 45)(18, 44)(19, 43)(20, 42)(21, 41)(22, 40)(23, 39)(24, 38)(25, 37)(26, 36)(27, 35)(28, 34)(29, 33)(30, 32)(61, 150)(62, 149)(63, 148)(64, 147)(65, 146)(66, 145)(67, 144)(68, 143)(69, 142)(70, 141)(71, 140)(72, 139)(73, 138)(74, 137)(75, 136)(76, 135)(77, 134)(78, 133)(79, 132)(80, 131)(81, 130)(82, 129)(83, 128)(84, 127)(85, 126)(86, 125)(87, 124)(88, 123)(89, 122)(90, 121)(91, 180)(92, 179)(93, 178)(94, 177)(95, 176)(96, 175)(97, 174)(98, 173)(99, 172)(100, 171)(101, 170)(102, 169)(103, 168)(104, 167)(105, 166)(106, 165)(107, 164)(108, 163)(109, 162)(110, 161)(111, 160)(112, 159)(113, 158)(114, 157)(115, 156)(116, 155)(117, 154)(118, 153)(119, 152)(120, 151)(181, 237)(182, 236)(183, 235)(184, 234)(185, 233)(186, 232)(187, 231)(188, 230)(189, 229)(190, 228)(191, 227)(192, 226)(193, 225)(194, 224)(195, 223)(196, 222)(197, 221)(198, 220)(199, 219)(200, 218)(201, 217)(202, 216)(203, 215)(204, 214)(205, 213)(206, 212)(207, 211)(208, 210)(238, 240)
b: (2, 60, 121, 90)(3, 89, 108, 237)(4, 236, 168, 177)(5, 176, 95, 57)(6, 56)(7, 55, 126, 85)(8, 84, 113, 232)(9, 231, 173, 172)(10, 171, 100, 52)(11, 51)(12, 50, 131, 80)(13, 79, 118, 227)(14, 226, 178, 167)(15, 166, 105, 47)(16, 46)(17, 45, 136, 75)(18, 74, 63, 222)(19, 221, 123, 162)(20, 161, 110, 42)(21, 41)(22, 40, 141, 70)(23, 69, 68, 217)(24, 216, 128, 157)(25, 156, 115, 37)(26, 36)(27, 35, 146, 65)(28, 64, 73, 212)(29, 211, 133, 152)(30, 151, 120, 32)(33, 119, 78, 207)(34, 206, 138, 147)(38, 114, 83, 202)(39, 201, 143, 142)(43, 109, 88, 197)(44, 196, 148, 137)(48, 104, 93, 192)(49, 191, 153, 132)(53, 99, 98, 187)(54, 186, 158, 127)(58, 94, 103, 182)(59, 181, 163, 122)(61, 150, 91, 180)(62, 179, 225, 223)(66, 145, 96, 175)(67, 174, 230, 218)(71, 140, 101, 170)(72, 169, 235, 213)(76, 135, 106, 165)(77, 164, 240, 208)(81, 130, 111, 160)(82, 159, 185, 203)(86, 125, 116, 155)(87, 154, 190, 198)(92, 149, 195, 193)(97, 144, 200, 188)(102, 139, 205, 183)(107, 134, 210, 238)(112, 129, 215, 233)(117, 124, 220, 228)(184, 204)(189, 199)(209, 239)(214, 234)(219, 229)
c: (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, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180)(181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240)

(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[ 240, 56 ]
240
-1 121 2 90 60
-2 1 122 3 91
-3 2 123 4 92
-4 3 124 5 93
-5 4 125 6 94
-6 5 126 7 95
-7 6 127 8 96
-8 7 128 9 97
-9 8 129 10 98
-10 11 99 9 130
-11 12 100 10 131
-12 11 132 13 101
-13 12 133 14 102
-14 13 134 15 103
-15 14 135 16 104
-16 15 136 17 105
-17 16 137 18 106
-18 17 138 19 107
-19 18 139 20 108
-20 19 140 21 109
-21 22 110 20 141
-22 23 111 21 142
-23 22 143 24 112
-24 23 144 25 113
-25 24 145 26 114
-26 25 146 27 115
-27 26 147 28 116
-28 27 148 29 117
-29 28 149 30 118
-30 29 150 31 119
-31 30 151 32 120
-32 33 61 31 152
-33 34 62 32 153
-34 33 154 35 63
-35 34 155 36 64
-36 35 156 37 65
-37 66 36 157 38
-38 67 37 158 39
-39 68 38 159 40
-40 69 39 160 41
-41 70 40 161 42
-42 71 41 162 43
-43 44 72 42 163
-44 45 73 43 164
-45 44 165 46 74
-46 45 166 47 75
-47 46 167 48 76
-48 77 47 168 49
-49 78 48 169 50
-50 79 49 170 51
-51 80 50 171 52
-52 81 51 172 53
-53 82 52 173 54
-54 55 83 53 174
-55 56 84 54 175
-56 55 176 57 85
-57 56 177 58 86
-58 57 178 59 87
-59 88 58 179 60
-60 1 89 59 180
-61 121 134 32 208
-62 33 209 122 135
-63 34 210 123 136
-64 35 211 124 137
-65 36 212 125 138
-66 37 213 126 139
-67 38 214 127 140
-68 39 215 128 141
-69 40 216 129 142
-70 143 41 217 130
-71 144 42 218 131
-72 132 145 43 219
-73 44 220 133 146
-74 45 221 134 147
-75 46 222 135 148
-76 47 223 136 149
-77 48 224 137 150
-78 49 225 138 151
-79 50 226 139 152
-80 51 227 140 153
-81 154 52 228 141
-82 155 53 229 142
-83 143 156 54 230
-84 55 231 144 157
-85 56 232 145 158
-86 57 233 146 159
-87 58 234 147 160
-88 59 235 148 161
-89 60 236 149 162
-90 1 237 150 163
-91 2 238 151 164
-92 165 3 239 152
-93 166 4 240 153
-94 154 167 5 181
-95 155 168 6 182
-96 156 169 7 183
-97 157 170 8 184
-98 158 171 9 185
-99 159 172 10 186
-100 11 187 160 173
-101 12 188 161 174
-102 13 189 162 175
-103 176 14 190 163
-104 177 15 191 164
-105 165 178 16 192
-106 166 179 17 193
-107 167 180 18 194
-108 121 168 19 195
-109 122 169 20 196
-110 123 170 21 197
-111 22 198 124 171
-112 23 199 125 172
-113 24 200 126 173
-114 25 201 127 174
-115 26 202 128 175
-116 176 27 203 129
-117 177 28 204 130
-118 178 29 205 131
-119 132 179 30 206
-120 133 180 31 207
-121 1 181 61 108
-122 2 182 62 109
-123 110 3 183 63
-124 111 4 184 64
-125 112 5 185 65
-126 66 113 6 186
-127 187 67 114 7
-128 188 68 115 8
-129 189 69 116 9
-130 190 70 117 10
-131 11 191 71 118
-132 12 192 72 119
-133 13 193 73 120
-134 14 61 194 74
-135 15 62 195 75
-136 16 63 196 76
-137 77 17 64 197
-138 198 78 18 65
-139 66 199 79 19
-140 67 200 80 20
-141 68 201 81 21
-142 22 69 202 82
-143 23 70 203 83
-144 24 71 204 84
-145 25 72 205 85
-146 26 73 206 86
-147 27 74 207 87
-148 88 28 75 208
-149 209 89 29 76
-150 77 210 90 30
-151 78 211 91 31
-152 79 212 92 32
-153 33 80 213 93
-154 34 81 214 94
-155 35 82 215 95
-156 36 83 216 96
-157 37 84 217 97
-158 38 85 218 98
-159 99 39 86 219
-160 220 100 40 87
-161 88 221 101 41
-162 89 222 102 42
-163 90 223 103 43
-164 44 91 224 104
-165 45 92 225 105
-166 46 93 226 106
-167 47 94 227 107
-168 48 95 228 108
-169 49 96 229 109
-170 110 50 97 230
-171 231 111 51 98
-172 99 232 112 52
-173 100 233 113 53
-174 101 234 114 54
-175 55 102 235 115
-176 56 103 236 116
-177 57 104 237 117
-178 58 105 238 118
-179 59 106 239 119
-180 60 107 240 120
-181 121 225 94 197
-182 198 122 226 95
-183 199 123 227 96
-184 200 124 228 97
-185 201 125 229 98
-186 99 202 126 230
-187 231 100 203 127
-188 232 101 204 128
-189 233 102 205 129
-190 234 103 206 130
-191 235 104 207 131
-192 132 236 105 208
-193 209 133 237 106
-194 210 134 238 107
-195 211 135 239 108
-196 212 136 240 109
-197 110 213 137 181
-198 111 214 138 182
-199 112 215 139 183
-200 113 216 140 184
-201 114 217 141 185
-202 115 218 142 186
-203 143 187 116 219
-204 220 144 188 117
-205 221 145 189 118
-206 222 146 190 119
-207 223 147 191 120
-208 224 148 192 61
-209 225 149 193 62
-210 226 150 194 63
-211 227 151 195 64
-212 228 152 196 65
-213 66 229 153 197
-214 154 198 67 230
-215 231 155 199 68
-216 232 156 200 69
-217 233 157 201 70
-218 234 158 202 71
-219 235 159 203 72
-220 236 160 204 73
-221 237 161 205 74
-222 238 162 206 75
-223 239 163 207 76
-224 77 240 164 208
-225 165 209 78 181
-226 166 210 79 182
-227 167 211 80 183
-228 168 212 81 184
-229 169 213 82 185
-230 170 214 83 186
-231 187 171 215 84
-232 188 172 216 85
-233 189 173 217 86
-234 190 174 218 87
-235 88 191 175 219
-236 176 220 89 192
-237 177 221 90 193
-238 178 222 91 194
-239 179 223 92 195
-240 180 224 93 196
0

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