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On this page are computer-accessible forms for the graph C4[ 256, 85 ] = UG(ATD[256,167]).

(I) Following is a form readable by MAGMA:

g:=Graph<256|{ {52, 53}, {234, 235}, {220, 221}, {214, 215}, {188, 189}, {90, 91}, {112, 113}, {118, 119}, {1, 3}, {44, 46}, {1, 2}, {244, 247}, {217, 218}, {180, 183}, {4, 7}, {96, 99}, {156, 159}, {25, 29}, {162, 166}, {3, 6}, {208, 213}, {67, 70}, {2, 4}, {2, 5}, {219, 220}, {5, 13}, {246, 254}, {245, 253}, {229, 237}, {215, 223}, {212, 220}, {211, 219}, {7, 15}, {6, 14}, {20, 29}, {230, 239}, {39, 45}, {245, 255}, {3, 8}, {240, 251}, {181, 190}, {7, 12}, {19, 31}, {242, 254}, {241, 253}, {240, 252}, {179, 191}, {64, 76}, {33, 45}, {129, 141}, {130, 142}, {131, 143}, {160, 172}, {4, 9}, {227, 238}, {182, 187}, {18, 31}, {16, 29}, {6, 11}, {99, 110}, {147, 158}, {150, 152}, {244, 250}, {241, 255}, {208, 222}, {5, 10}, {230, 233}, {71, 72}, {17, 30}, {98, 109}, {169, 184}, {232, 249}, {227, 242}, {32, 50}, {231, 245}, {170, 184}, {71, 85}, {33, 51}, {107, 121}, {11, 24}, {239, 252}, {15, 28}, {99, 112}, {138, 153}, {162, 177}, {76, 88}, {239, 251}, {229, 241}, {205, 217}, {197, 209}, {108, 120}, {12, 25}, {226, 247}, {224, 245}, {14, 27}, {139, 158}, {140, 153}, {46, 56}, {70, 80}, {13, 26}, {225, 246}, {207, 216}, {198, 209}, {64, 87}, {8, 16}, {226, 250}, {225, 249}, {224, 248}, {12, 20}, {11, 19}, {10, 18}, {9, 17}, {135, 158}, {193, 218}, {235, 240}, {32, 60}, {35, 63}, {34, 62}, {33, 61}, {8, 21}, {41, 52}, {35, 62}, {34, 63}, {10, 23}, {197, 219}, {232, 246}, {9, 22}, {231, 248}, {132, 164}, {196, 228}, {133, 165}, {134, 166}, {135, 167}, {21, 52}, {199, 230}, {78, 111}, {66, 99}, {27, 58}, {25, 56}, {23, 54}, {132, 165}, {133, 164}, {157, 191}, {203, 233}, {202, 232}, {201, 235}, {199, 229}, {198, 228}, {22, 53}, {193, 226}, {75, 104}, {65, 98}, {26, 57}, {138, 169}, {154, 185}, {155, 184}, {203, 239}, {214, 242}, {155, 190}, {212, 241}, {198, 227}, {94, 120}, {204, 234}, {202, 236}, {139, 173}, {28, 59}, {196, 227}, {93, 122}, {92, 123}, {88, 127}, {80, 119}, {67, 100}, {154, 189}, {144, 184}, {145, 185}, {146, 186}, {147, 187}, {148, 188}, {81, 120}, {87, 126}, {85, 124}, {83, 122}, {75, 97}, {222, 244}, {152, 178}, {15, 36}, {223, 244}, {86, 125}, {82, 121}, {73, 101}, {223, 243}, {205, 225}, {145, 189}, {156, 176}, {14, 35}, {222, 243}, {200, 229}, {74, 103}, {72, 101}, {95, 114}, {30, 48}, {201, 231}, {200, 230}, {72, 102}, {31, 49}, {13, 34}, {207, 224}, {91, 116}, {84, 123}, {78, 97}, {73, 102}, {31, 48}, {30, 49}, {24, 55}, {65, 112}, {67, 114}, {1, 51}, {18, 32}, {19, 32}, {91, 104}, {90, 105}, {66, 113}, {28, 47}, {24, 43}, {20, 39}, {159, 171}, {16, 37}, {210, 231}, {27, 46}, {25, 44}, {20, 33}, {135, 178}, {151, 161}, {17, 38}, {86, 97}, {26, 45}, {134, 177}, {149, 162}, {77, 117}, {214, 238}, {140, 180}, {141, 181}, {142, 182}, {143, 183}, {74, 115}, {212, 237}, {210, 235}, {79, 118}, {151, 174}, {79, 117}, {137, 179}, {149, 175}, {77, 118}, {217, 226}, {211, 232}, {95, 100}, {141, 182}, {142, 181}, {204, 240}, {21, 40}, {23, 42}, {95, 98}, {137, 180}, {157, 160}, {150, 168}, {22, 41}, {211, 236}, {75, 116}, {140, 179}, {152, 167}, {156, 163}, {143, 196}, {1, 76}, {56, 105}, {62, 111}, {60, 109}, {58, 107}, {155, 201}, {57, 106}, {61, 110}, {146, 198}, {147, 199}, {144, 197}, {59, 108}, {157, 202}, {186, 224}, {148, 200}, {61, 96}, {188, 225}, {62, 97}, {163, 193}, {186, 216}, {56, 91}, {172, 207}, {60, 95}, {163, 192}, {36, 64}, {178, 214}, {177, 213}, {176, 212}, {171, 207}, {170, 206}, {44, 72}, {39, 67}, {38, 66}, {37, 65}, {164, 192}, {47, 74}, {188, 217}, {168, 205}, {166, 195}, {59, 94}, {57, 92}, {55, 82}, {50, 87}, {164, 193}, {47, 73}, {168, 206}, {49, 86}, {170, 205}, {58, 93}, {165, 194}, {36, 77}, {38, 79}, {2, 104}, {166, 204}, {3, 104}, {186, 209}, {185, 210}, {51, 88}, {37, 78}, {40, 68}, {169, 197}, {54, 90}, {53, 89}, {43, 71}, {42, 70}, {41, 69}, {176, 221}, {178, 223}, {165, 203}, {185, 215}, {53, 90}, {177, 222}, {54, 89}, {180, 196}, {182, 199}, {55, 69}, {63, 77}, {175, 220}, {138, 254}, {191, 203}, {183, 195}, {189, 200}, {50, 68}, {173, 219}, {51, 69}, {39, 80}, {60, 68}, {61, 69}, {40, 81}, {179, 202}, {174, 215}, {48, 73}, {44, 85}, {42, 83}, {48, 74}, {49, 75}, {41, 82}, {183, 204}, {171, 208}, {172, 208}, {181, 201}, {175, 211}, {174, 210}, {173, 209}, {191, 194}, {50, 76}, {43, 84}, {63, 64}, {120, 254}, {112, 250}, {4, 136}, {5, 136}, {106, 255}, {107, 253}, {98, 250}, {7, 167}, {93, 253}, {92, 255}, {6, 161}, {83, 251}, {84, 252}, {8, 161}, {9, 167}, {68, 234}, {11, 187}, {13, 190}, {10, 190}, {14, 187}, {78, 248}, {65, 248}, {71, 252}, {81, 234}, {70, 251}, {23, 213}, {43, 238}, {34, 228}, {110, 168}, {111, 169}, {18, 213}, {17, 216}, {89, 144}, {58, 243}, {36, 237}, {15, 195}, {59, 247}, {22, 216}, {12, 195}, {54, 249}, {38, 233}, {35, 236}, {94, 145}, {127, 176}, {83, 130}, {113, 160}, {126, 175}, {124, 174}, {19, 192}, {42, 249}, {84, 129}, {88, 143}, {24, 192}, {47, 247}, {114, 170}, {115, 171}, {116, 172}, {117, 173}, {55, 238}, {89, 128}, {87, 142}, {85, 140}, {82, 139}, {80, 137}, {122, 160}, {21, 206}, {86, 141}, {81, 138}, {126, 162}, {127, 163}, {46, 243}, {92, 129}, {94, 131}, {124, 161}, {16, 206}, {29, 194}, {93, 130}, {101, 133}, {107, 139}, {122, 154}, {100, 133}, {102, 135}, {100, 134}, {57, 218}, {101, 134}, {119, 148}, {96, 132}, {124, 153}, {121, 159}, {37, 194}, {103, 128}, {52, 221}, {114, 155}, {116, 157}, {106, 128}, {123, 145}, {113, 154}, {117, 158}, {121, 151}, {103, 136}, {115, 156}, {125, 146}, {28, 237}, {96, 146}, {109, 159}, {103, 148}, {115, 128}, {40, 221}, {102, 147}, {110, 152}, {111, 153}, {27, 236}, {45, 218}, {30, 233}, {123, 131}, {108, 149}, {125, 132}, {106, 144}, {108, 150}, {109, 151}, {105, 149}, {125, 129}, {126, 130}, {127, 131}, {26, 228}, {105, 150}, {118, 137}, {119, 136}, {66, 256}, {79, 256}, {242, 256}, {246, 256} }>;

(II) A more general form is to represent the graph as the orbit of {52, 53} under the group generated by the following permutations:

a: (1, 2, 4, 7, 12, 20, 33, 51)(3, 5, 9, 15, 25, 39, 61, 88)(6, 10, 17, 28, 44, 67, 96, 127)(8, 13, 22, 36, 56, 80, 110, 143)(11, 18, 30, 47, 72, 100, 132, 163)(14, 23, 38, 59, 85, 114, 146, 176)(16, 26, 41, 64, 91, 119, 152, 183)(19, 31, 48, 73, 101, 133, 164, 192)(21, 34, 53, 77, 105, 137, 168, 196)(24, 32, 49, 74, 102, 134, 165, 193)(27, 42, 66, 94, 124, 155, 186, 212)(29, 45, 69, 76, 104, 136, 167, 195)(35, 54, 79, 108, 140, 170, 198, 221)(37, 57, 82, 87, 116, 148, 178, 204)(40, 62, 89, 117, 149, 179, 205, 227)(43, 60, 86, 115, 147, 177, 203, 226)(46, 70, 99, 131, 161, 190, 216, 237)(50, 75, 103, 135, 166, 194, 218, 55)(52, 63, 90, 118, 150, 180, 206, 228)(58, 83, 113, 145, 174, 201, 224, 241)(65, 92, 121, 142, 172, 200, 223, 240)(68, 97, 128, 158, 162, 191, 217, 238)(71, 95, 125, 156, 187, 213, 233, 247)(78, 106, 139, 126, 157, 188, 214, 234)(81, 111, 144, 173, 175, 202, 225, 242)(84, 109, 141, 171, 199, 222, 239, 250)(93, 122, 154, 185, 210, 231, 245, 253)(98, 129, 159, 182, 208, 230, 244, 252)(107, 130, 160, 189, 215, 235, 248, 255)(112, 123, 151, 181, 207, 229, 243, 251)(120, 153, 184, 209, 220, 236, 249, 256)(138, 169, 197, 219, 211, 232, 246, 254)
b: (2, 51)(3, 76)(4, 33)(5, 69)(6, 50)(7, 20)(8, 64)(9, 45)(10, 55)(11, 32)(13, 41)(14, 68)(15, 29)(16, 36)(17, 218)(18, 24)(21, 63)(22, 26)(23, 238)(25, 195)(27, 234)(28, 194)(30, 193)(31, 192)(34, 52)(35, 40)(37, 237)(38, 217)(39, 167)(42, 214)(43, 213)(44, 166)(46, 204)(47, 165)(48, 164)(49, 163)(53, 228)(54, 227)(56, 183)(57, 216)(58, 235)(59, 191)(60, 187)(61, 136)(62, 221)(65, 229)(66, 188)(67, 135)(70, 178)(71, 177)(72, 134)(73, 133)(74, 132)(75, 127)(77, 206)(78, 212)(79, 205)(80, 152)(81, 236)(82, 190)(83, 215)(84, 208)(85, 162)(86, 156)(87, 161)(88, 104)(89, 198)(90, 196)(91, 143)(92, 207)(93, 210)(94, 157)(95, 147)(96, 103)(97, 176)(98, 199)(99, 148)(100, 102)(105, 180)(106, 186)(107, 201)(108, 179)(109, 182)(110, 119)(111, 220)(112, 200)(113, 189)(114, 158)(115, 125)(116, 131)(117, 170)(118, 168)(120, 202)(121, 181)(122, 185)(123, 172)(124, 126)(128, 146)(129, 171)(130, 174)(137, 150)(138, 211)(139, 155)(140, 149)(141, 159)(142, 151)(144, 209)(145, 160)(153, 175)(169, 219)(173, 184)(203, 247)(222, 252)(223, 251)(224, 255)(225, 256)(226, 233)(230, 250)(231, 253)(232, 254)(239, 244)(240, 243)(241, 248)(242, 249)
c: (2, 3)(4, 6)(5, 8)(7, 11)(9, 14)(10, 16)(12, 19)(13, 21)(15, 24)(17, 27)(18, 29)(20, 32)(22, 35)(23, 37)(25, 31)(26, 40)(28, 43)(30, 46)(33, 50)(34, 52)(36, 55)(38, 58)(39, 60)(41, 63)(42, 65)(44, 48)(45, 68)(47, 71)(49, 56)(51, 76)(53, 62)(54, 78)(57, 81)(59, 84)(61, 87)(64, 69)(66, 93)(67, 95)(70, 98)(72, 73)(74, 85)(75, 91)(77, 82)(79, 107)(80, 109)(83, 112)(86, 105)(89, 111)(90, 97)(92, 120)(94, 123)(96, 126)(99, 130)(103, 124)(106, 138)(108, 129)(110, 142)(113, 122)(115, 140)(117, 139)(118, 121)(119, 151)(125, 149)(127, 143)(128, 153)(132, 162)(133, 134)(135, 147)(136, 161)(137, 159)(141, 150)(144, 169)(146, 175)(148, 174)(152, 182)(155, 170)(156, 180)(157, 172)(163, 183)(164, 166)(165, 177)(167, 187)(168, 181)(171, 179)(176, 196)(178, 199)(185, 189)(186, 211)(188, 210)(190, 206)(191, 208)(192, 195)(193, 204)(194, 213)(198, 220)(200, 215)(201, 205)(202, 207)(203, 222)(209, 219)(212, 227)(214, 229)(216, 236)(217, 235)(218, 234)(221, 228)(223, 230)(224, 232)(225, 231)(226, 240)(233, 243)(237, 238)(239, 244)(241, 242)(245, 246)(247, 252)(248, 249)(250, 251)(253, 256)(254, 255)
d: (4, 5)(6, 8)(7, 13)(9, 10)(11, 21)(12, 34)(14, 16)(15, 26)(17, 23)(18, 22)(19, 52)(20, 63)(24, 40)(25, 62)(27, 37)(28, 57)(29, 35)(30, 54)(31, 53)(32, 41)(33, 64)(36, 45)(38, 42)(39, 77)(43, 81)(44, 111)(46, 78)(47, 106)(48, 89)(49, 90)(50, 69)(51, 76)(55, 68)(56, 97)(58, 65)(59, 92)(60, 82)(61, 87)(66, 83)(67, 117)(70, 79)(71, 138)(72, 169)(73, 144)(74, 128)(75, 91)(80, 118)(84, 120)(85, 153)(86, 105)(93, 112)(94, 123)(95, 139)(96, 126)(98, 107)(99, 130)(100, 173)(101, 197)(102, 184)(108, 129)(109, 121)(110, 142)(113, 122)(114, 158)(125, 149)(132, 175)(133, 219)(134, 209)(135, 155)(141, 150)(146, 162)(147, 170)(152, 181)(163, 176)(164, 220)(165, 211)(166, 198)(167, 190)(168, 182)(177, 186)(178, 201)(183, 196)(187, 206)(188, 200)(191, 202)(192, 221)(193, 212)(194, 236)(195, 228)(199, 205)(203, 232)(204, 227)(207, 208)(210, 215)(213, 216)(214, 235)(217, 229)(218, 237)(222, 224)(223, 231)(225, 230)(226, 241)(233, 249)(234, 238)(239, 246)(240, 242)(243, 248)(244, 245)(247, 255)(250, 253)(251, 256)(252, 254)

(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[ 256, 85 ]
256
-1 2 3 51 76
-2 1 4 5 104
-3 1 104 6 8
-4 2 136 7 9
-5 2 13 136 10
-6 11 3 14 161
-7 12 167 4 15
-8 3 16 161 21
-9 22 167 4 17
-10 23 190 5 18
-11 187 24 6 19
-12 25 7 195 20
-13 34 190 26 5
-14 187 35 27 6
-15 36 28 7 195
-16 37 29 8 206
-17 38 216 30 9
-18 213 31 10 32
-19 11 192 31 32
-20 33 12 39 29
-21 40 8 52 206
-22 216 41 9 53
-23 213 42 10 54
-24 11 55 192 43
-25 44 12 56 29
-26 45 13 57 228
-27 46 14 58 236
-28 47 15 59 237
-29 25 16 194 20
-30 233 48 49 17
-31 48 49 18 19
-32 60 50 18 19
-33 45 61 51 20
-34 13 62 63 228
-35 14 236 62 63
-36 77 15 237 64
-37 78 16 194 65
-38 66 79 233 17
-39 45 67 80 20
-40 221 68 81 21
-41 22 69 82 52
-42 23 70 83 249
-43 24 71 84 238
-44 46 25 72 85
-45 33 26 39 218
-46 44 56 243 27
-47 247 28 73 74
-48 73 30 74 31
-49 30 31 75 86
-50 68 32 76 87
-51 33 88 1 69
-52 221 41 53 21
-53 22 89 90 52
-54 23 89 90 249
-55 24 69 82 238
-56 46 25 91 105
-57 26 92 106 218
-58 243 27 93 107
-59 247 28 94 108
-60 68 95 32 109
-61 33 110 69 96
-62 34 111 35 97
-63 77 34 35 64
-64 36 63 76 87
-65 112 37 248 98
-66 99 113 256 38
-67 100 70 114 39
-68 234 60 50 40
-69 55 61 51 41
-70 67 80 42 251
-71 72 85 43 252
-72 44 101 102 71
-73 101 47 102 48
-74 47 48 103 115
-75 49 104 116 97
-76 88 1 50 64
-77 36 117 63 118
-78 111 37 248 97
-79 256 38 117 118
-80 70 137 39 119
-81 234 138 40 120
-82 55 121 139 41
-83 122 42 130 251
-84 123 129 43 252
-85 44 124 71 140
-86 125 49 97 141
-87 126 50 64 142
-88 143 127 51 76
-89 144 128 53 54
-90 91 105 53 54
-91 56 90 104 116
-92 57 123 255 129
-93 253 122 58 130
-94 145 59 120 131
-95 100 114 60 98
-96 99 132 146 61
-97 78 62 75 86
-98 95 250 65 109
-99 66 110 112 96
-100 67 133 134 95
-101 133 134 72 73
-102 135 147 72 73
-103 136 148 128 74
-104 2 3 91 75
-105 56 90 149 150
-106 144 57 255 128
-107 121 253 58 139
-108 59 149 150 120
-109 60 159 151 98
-110 99 168 61 152
-111 78 169 62 153
-112 99 113 250 65
-113 66 154 112 160
-114 67 155 170 95
-115 156 171 128 74
-116 91 157 172 75
-117 77 79 158 173
-118 77 79 137 119
-119 80 136 148 118
-120 254 81 94 108
-121 82 159 107 151
-122 154 93 83 160
-123 145 92 84 131
-124 161 85 174 153
-125 132 146 129 86
-126 162 130 87 175
-127 88 176 163 131
-128 89 103 115 106
-129 92 125 84 141
-130 93 126 83 142
-131 143 123 94 127
-132 165 125 96 164
-133 165 100 101 164
-134 100 166 177 101
-135 167 178 102 158
-136 4 103 5 119
-137 80 179 180 118
-138 254 81 169 153
-139 158 82 107 173
-140 179 180 85 153
-141 181 182 129 86
-142 181 182 130 87
-143 88 183 196 131
-144 89 106 184 197
-145 123 189 94 185
-146 198 125 96 186
-147 187 199 102 158
-148 188 200 103 119
-149 105 162 108 175
-150 168 105 108 152
-151 121 161 174 109
-152 110 167 178 150
-153 111 124 138 140
-154 122 189 113 185
-155 190 201 114 184
-156 176 115 159 163
-157 191 202 116 160
-158 135 147 117 139
-159 121 156 171 109
-160 122 113 157 172
-161 124 6 8 151
-162 166 177 126 149
-163 156 192 127 193
-164 132 133 192 193
-165 132 133 203 194
-166 134 204 162 195
-167 135 7 9 152
-168 110 150 205 206
-169 111 138 184 197
-170 114 205 184 206
-171 115 159 207 208
-172 116 160 207 208
-173 209 117 139 219
-174 210 124 215 151
-175 220 211 126 149
-176 221 156 212 127
-177 134 222 213 162
-178 135 223 214 152
-179 191 202 137 140
-180 137 183 140 196
-181 190 201 141 142
-182 187 199 141 142
-183 143 180 204 195
-184 144 155 169 170
-185 154 210 145 215
-186 209 146 224 216
-187 11 14 147 182
-188 189 148 225 217
-189 154 188 145 200
-190 155 13 181 10
-191 157 179 203 194
-192 24 19 163 164
-193 226 163 218 164
-194 165 37 191 29
-195 12 166 15 183
-196 143 180 227 228
-197 209 144 169 219
-198 209 146 227 228
-199 147 182 229 230
-200 189 148 229 230
-201 231 155 235 181
-202 232 157 179 236
-203 165 233 191 239
-204 166 234 183 240
-205 168 170 225 217
-206 168 16 170 21
-207 224 171 172 216
-208 222 213 171 172
-209 198 173 186 197
-210 231 235 174 185
-211 232 236 175 219
-212 176 220 237 241
-213 23 177 18 208
-214 242 178 215 238
-215 223 214 174 185
-216 22 17 207 186
-217 188 226 205 218
-218 45 57 193 217
-219 220 211 173 197
-220 221 212 175 219
-221 176 220 40 52
-222 177 243 244 208
-223 243 178 244 215
-224 245 248 207 186
-225 188 246 205 249
-226 247 193 217 250
-227 198 242 238 196
-228 198 34 26 196
-229 199 200 237 241
-230 199 200 233 239
-231 210 201 245 248
-232 211 202 246 249
-233 38 203 30 230
-234 68 81 235 204
-235 210 201 234 240
-236 35 211 202 27
-237 36 212 28 229
-238 55 214 227 43
-239 203 251 230 252
-240 235 204 251 252
-241 253 255 212 229
-242 254 256 214 227
-243 46 222 58 223
-244 222 223 247 250
-245 231 253 255 224
-246 232 254 256 225
-247 244 47 59 226
-248 231 78 224 65
-249 232 225 42 54
-250 112 244 226 98
-251 70 83 239 240
-252 71 84 239 240
-253 245 93 107 241
-254 242 246 138 120
-255 245 92 106 241
-256 66 242 79 246
0

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