C4graphGraph forms for C4 [ 222, 2 ] = C_222(1,73)

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On this page are computer-accessible forms for the graph C4[ 222, 2 ] = C_222(1,73).

(I) Following is a form readable by MAGMA:

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

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

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

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