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On this page are computer-accessible forms for the graph C4[ 274, 1 ] = W(137,2).

(I) Following is a form readable by MAGMA:

g:=Graph<274|{ {2, 3}, {272, 273}, {270, 271}, {268, 269}, {266, 267}, {264, 265}, {262, 263}, {260, 261}, {258, 259}, {256, 257}, {254, 255}, {252, 253}, {250, 251}, {248, 249}, {246, 247}, {244, 245}, {242, 243}, {240, 241}, {238, 239}, {236, 237}, {234, 235}, {232, 233}, {230, 231}, {228, 229}, {226, 227}, {224, 225}, {222, 223}, {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}, {84, 85}, {82, 83}, {80, 81}, {78, 79}, {76, 77}, {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}, {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}, {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}, {1, 2}, {273, 274}, {269, 270}, {265, 266}, {261, 262}, {257, 258}, {253, 254}, {249, 250}, {245, 246}, {241, 242}, {237, 238}, {233, 234}, {229, 230}, {225, 226}, {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}, {81, 82}, {77, 78}, {73, 74}, {69, 70}, {65, 66}, {61, 62}, {57, 58}, {53, 54}, {5, 6}, {9, 10}, {13, 14}, {17, 18}, {21, 22}, {25, 26}, {29, 30}, {33, 34}, {37, 38}, {41, 42}, {45, 46}, {49, 50}, {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}, {145, 146}, {149, 150}, {153, 154}, {157, 158}, {161, 162}, {165, 166}, {3, 4}, {267, 268}, {259, 260}, {251, 252}, {243, 244}, {235, 236}, {227, 228}, {219, 220}, {211, 212}, {203, 204}, {195, 196}, {187, 188}, {179, 180}, {171, 172}, {83, 84}, {75, 76}, {67, 68}, {59, 60}, {51, 52}, {11, 12}, {19, 20}, {27, 28}, {35, 36}, {43, 44}, {91, 92}, {99, 100}, {107, 108}, {115, 116}, {123, 124}, {131, 132}, {139, 140}, {147, 148}, {155, 156}, {163, 164}, {7, 8}, {263, 264}, {247, 248}, {231, 232}, {215, 216}, {199, 200}, {183, 184}, {167, 168}, {71, 72}, {55, 56}, {23, 24}, {39, 40}, {87, 88}, {103, 104}, {119, 120}, {135, 136}, {151, 152}, {15, 16}, {271, 272}, {239, 240}, {207, 208}, {175, 176}, {79, 80}, {47, 48}, {111, 112}, {143, 144}, {31, 32}, {223, 224}, {95, 96}, {159, 160}, {63, 64}, {191, 192}, {1, 137}, {84, 220}, {83, 219}, {82, 218}, {81, 217}, {80, 216}, {71, 207}, {70, 206}, {69, 205}, {68, 204}, {67, 203}, {66, 202}, {65, 201}, {64, 200}, {55, 191}, {54, 190}, {53, 189}, {52, 188}, {51, 187}, {50, 186}, {2, 138}, {3, 139}, {4, 140}, {5, 141}, {6, 142}, {7, 143}, {16, 152}, {17, 153}, {18, 154}, {19, 155}, {20, 156}, {21, 157}, {22, 158}, {23, 159}, {32, 168}, {33, 169}, {34, 170}, {35, 171}, {36, 172}, {37, 173}, {38, 174}, {39, 175}, {48, 184}, {49, 185}, {85, 221}, {86, 222}, {87, 223}, {96, 232}, {97, 233}, {98, 234}, {99, 235}, {100, 236}, {101, 237}, {102, 238}, {103, 239}, {112, 248}, {113, 249}, {114, 250}, {115, 251}, {116, 252}, {117, 253}, {118, 254}, {119, 255}, {1, 139}, {84, 222}, {81, 219}, {80, 218}, {69, 207}, {68, 206}, {65, 203}, {64, 202}, {53, 191}, {52, 190}, {4, 142}, {5, 143}, {16, 154}, {17, 155}, {20, 158}, {21, 159}, {32, 170}, {33, 171}, {36, 174}, {37, 175}, {48, 186}, {49, 187}, {85, 223}, {96, 234}, {97, 235}, {100, 238}, {101, 239}, {112, 250}, {113, 251}, {116, 254}, {117, 255}, {2, 140}, {83, 221}, {82, 220}, {67, 205}, {66, 204}, {51, 189}, {50, 188}, {3, 141}, {18, 156}, {19, 157}, {34, 172}, {35, 173}, {98, 236}, {99, 237}, {114, 252}, {115, 253}, {6, 144}, {79, 217}, {78, 216}, {71, 209}, {70, 208}, {7, 145}, {14, 152}, {15, 153}, {38, 176}, {39, 177}, {46, 184}, {47, 185}, {102, 240}, {103, 241}, {110, 248}, {111, 249}, {8, 144}, {79, 215}, {78, 214}, {77, 213}, {76, 212}, {75, 211}, {74, 210}, {73, 209}, {72, 208}, {9, 145}, {10, 146}, {11, 147}, {12, 148}, {13, 149}, {14, 150}, {15, 151}, {40, 176}, {41, 177}, {42, 178}, {43, 179}, {44, 180}, {45, 181}, {46, 182}, {47, 183}, {104, 240}, {105, 241}, {106, 242}, {107, 243}, {108, 244}, {109, 245}, {110, 246}, {111, 247}, {8, 146}, {77, 215}, {76, 214}, {73, 211}, {72, 210}, {9, 147}, {12, 150}, {13, 151}, {40, 178}, {41, 179}, {44, 182}, {45, 183}, {104, 242}, {105, 243}, {108, 246}, {109, 247}, {10, 148}, {75, 213}, {74, 212}, {11, 149}, {42, 180}, {43, 181}, {106, 244}, {107, 245}, {22, 160}, {23, 161}, {30, 168}, {31, 169}, {86, 224}, {87, 225}, {94, 232}, {95, 233}, {24, 160}, {25, 161}, {26, 162}, {27, 163}, {28, 164}, {29, 165}, {30, 166}, {31, 167}, {88, 224}, {89, 225}, {90, 226}, {91, 227}, {92, 228}, {93, 229}, {94, 230}, {95, 231}, {24, 162}, {25, 163}, {28, 166}, {29, 167}, {88, 226}, {89, 227}, {92, 230}, {93, 231}, {26, 164}, {27, 165}, {90, 228}, {91, 229}, {54, 192}, {63, 201}, {62, 200}, {55, 193}, {56, 192}, {63, 199}, {62, 198}, {61, 197}, {60, 196}, {59, 195}, {58, 194}, {57, 193}, {56, 194}, {61, 199}, {60, 198}, {57, 195}, {58, 196}, {59, 197}, {127, 128}, {1, 274}, {118, 256}, {119, 257}, {126, 264}, {127, 265}, {120, 256}, {121, 257}, {122, 258}, {123, 259}, {124, 260}, {125, 261}, {126, 262}, {127, 263}, {120, 258}, {121, 259}, {124, 262}, {125, 263}, {122, 260}, {123, 261}, {128, 264}, {129, 265}, {130, 266}, {131, 267}, {132, 268}, {133, 269}, {134, 270}, {135, 271}, {128, 266}, {129, 267}, {132, 270}, {133, 271}, {130, 268}, {131, 269}, {134, 272}, {135, 273}, {136, 272}, {137, 273}, {138, 274}, {136, 274}, {255, 256} }>;

(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: (56, 193)
b: (121, 258)
c: (11, 148)
d: (75, 212)
e: (2, 137)(3, 136)(4, 135)(5, 134)(6, 133)(7, 132)(8, 131)(9, 130)(10, 129)(11, 128)(12, 127)(13, 126)(14, 125)(15, 124)(16, 123)(17, 122)(18, 121)(19, 120)(20, 119)(21, 118)(22, 117)(23, 116)(24, 115)(25, 114)(26, 113)(27, 112)(28, 111)(29, 110)(30, 109)(31, 108)(32, 107)(33, 106)(34, 105)(35, 104)(36, 103)(37, 102)(38, 101)(39, 100)(40, 99)(41, 98)(42, 97)(43, 96)(44, 95)(45, 94)(46, 93)(47, 92)(48, 91)(49, 90)(50, 89)(51, 88)(52, 87)(53, 86)(54, 85)(55, 84)(56, 83)(57, 82)(58, 81)(59, 80)(60, 79)(61, 78)(62, 77)(63, 76)(64, 75)(65, 74)(66, 73)(67, 72)(68, 71)(69, 70)(139, 274)(140, 273)(141, 272)(142, 271)(143, 270)(144, 269)(145, 268)(146, 267)(147, 266)(148, 265)(149, 264)(150, 263)(151, 262)(152, 261)(153, 260)(154, 259)(155, 258)(156, 257)(157, 256)(158, 255)(159, 254)(160, 253)(161, 252)(162, 251)(163, 250)(164, 249)(165, 248)(166, 247)(167, 246)(168, 245)(169, 244)(170, 243)(171, 242)(172, 241)(173, 240)(174, 239)(175, 238)(176, 237)(177, 236)(178, 235)(179, 234)(180, 233)(181, 232)(182, 231)(183, 230)(184, 229)(185, 228)(186, 227)(187, 226)(188, 225)(189, 224)(190, 223)(191, 222)(192, 221)(193, 220)(194, 219)(195, 218)(196, 217)(197, 216)(198, 215)(199, 214)(200, 213)(201, 212)(202, 211)(203, 210)(204, 209)(205, 208)(206, 207)
f: (33, 170)
g: (97, 234)
h: (28, 165)
m: (92, 229)
n1: (58, 195)
a1: (120, 257)
b1: (114, 251)
c1: (50, 187)
d1: (6, 143)
e1: (130, 267)
f1: (70, 207)
g1: (3, 140)
h1: (67, 204)
m1: (115, 252)
n2: (51, 188)
a2: (112, 249)
b2: (41, 178)
c2: (105, 242)
d2: (48, 185)
e2: (7, 144)
f2: (71, 208)
g2: (42, 179)
h2: (106, 243)
m2: (118, 255)
n3: (132, 269)
a3: (54, 191)
b3: (23, 160)
c3: (87, 224)
d3: (124, 261)
e3: (30, 167)
f3: (46, 183)
g3: (110, 247)
h3: (94, 231)
m3: (65, 202)
n4: (129, 266)
a4: (31, 168)
b4: (95, 232)
c4: (128, 265)
d4: (136, 273)
e4: (59, 196)
f4: (113, 250)
g4: (49, 186)
h4: (61, 198)
m4: (26, 163)
n5: (90, 227)
a5: (63, 200)
b5: (101, 238)
c5: (37, 174)
d5: (125, 262)
e5: (22, 159)
f5: (86, 223)
g5: (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, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274)
h5: (119, 256)
m5: (55, 192)
n6: (15, 152)
a6: (79, 216)
b6: (123, 260)
c6: (29, 166)
d6: (93, 230)
e6: (16, 153)
f6: (80, 217)
g6: (116, 253)
h6: (52, 189)
m6: (21, 158)
n7: (85, 222)
a7: (137, 274)
b7: (13, 150)
c7: (74, 211)
d7: (10, 147)
e7: (77, 214)
f7: (20, 157)
g7: (84, 221)
h7: (57, 194)
m7: (135, 272)
n8: (8, 145)
a8: (72, 209)
b8: (109, 246)
c8: (45, 182)
d8: (43, 180)
e8: (107, 244)
f8: (62, 199)
g8: (9, 146)
h8: (73, 210)
m8: (27, 164)
n9: (91, 228)
a9: (126, 263)
b9: (131, 268)
c9: (102, 239)
d9: (38, 175)
e9: (66, 203)
f9: (2, 139)
g9: (104, 241)
h9: (40, 177)
m9: (117, 254)
n10: (53, 190)
a10: (24, 161)
b10: (88, 225)
c10: (14, 151)
d10: (89, 226)
e10: (25, 162)
f10: (39, 176)
g10: (103, 240)
h10: (78, 215)
m10: (17, 154)
n11: (81, 218)
a11: (122, 259)
b11: (5, 142)
c11: (69, 206)
d11: (60, 197)
e11: (64, 201)
f11: (133, 270)
g11: (18, 155)
h11: (82, 219)
m11: (4, 141)
n12: (134, 271)
a12: (35, 172)
b12: (99, 236)
c12: (19, 156)
d12: (83, 220)
e12: (32, 169)
f12: (96, 233)
g12: (36, 173)
h12: (100, 237)
m12: (34, 171)
n13: (98, 235)
a13: (108, 245)
b13: (44, 181)
c13: (12, 149)
d13: (47, 184)
e13: (111, 248)
f13: (76, 213)
g13: (127, 264)

(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[ 274, 1 ]
274
-1 2 137 139 274
-2 1 3 138 140
-3 2 4 139 141
-4 3 5 140 142
-5 143 4 6 141
-6 144 5 7 142
-7 143 145 6 8
-8 144 146 7 9
-9 145 147 8 10
-10 11 146 148 9
-11 12 147 149 10
-12 11 13 148 150
-13 12 14 149 151
-14 13 15 150 152
-15 14 16 151 153
-16 154 15 17 152
-17 155 16 18 153
-18 154 156 17 19
-19 155 157 18 20
-20 156 158 19 21
-21 22 157 159 20
-22 23 158 160 21
-23 22 24 159 161
-24 23 25 160 162
-25 24 26 161 163
-26 25 27 162 164
-27 165 26 28 163
-28 166 27 29 164
-29 165 167 28 30
-30 166 168 29 31
-31 167 169 30 32
-32 33 168 170 31
-33 34 169 171 32
-34 33 35 170 172
-35 34 36 171 173
-36 35 37 172 174
-37 36 38 173 175
-38 176 37 39 174
-39 177 38 40 175
-40 176 178 39 41
-41 177 179 40 42
-42 178 180 41 43
-43 44 179 181 42
-44 45 180 182 43
-45 44 46 181 183
-46 45 47 182 184
-47 46 48 183 185
-48 47 49 184 186
-49 187 48 50 185
-50 188 49 51 186
-51 187 189 50 52
-52 188 190 51 53
-53 189 191 52 54
-54 55 190 192 53
-55 56 191 193 54
-56 55 57 192 194
-57 56 58 193 195
-58 57 59 194 196
-59 58 60 195 197
-60 198 59 61 196
-61 199 60 62 197
-62 198 200 61 63
-63 199 201 62 64
-64 200 202 63 65
-65 66 201 203 64
-66 67 202 204 65
-67 66 68 203 205
-68 67 69 204 206
-69 68 70 205 207
-70 69 71 206 208
-71 209 70 72 207
-72 210 71 73 208
-73 209 211 72 74
-74 210 212 73 75
-75 211 213 74 76
-76 77 212 214 75
-77 78 213 215 76
-78 77 79 214 216
-79 78 80 215 217
-80 79 81 216 218
-81 80 82 217 219
-82 220 81 83 218
-83 221 82 84 219
-84 220 222 83 85
-85 221 223 84 86
-86 222 224 85 87
-87 88 223 225 86
-88 89 224 226 87
-89 88 90 225 227
-90 89 91 226 228
-91 90 92 227 229
-92 91 93 228 230
-93 231 92 94 229
-94 232 93 95 230
-95 231 233 94 96
-96 232 234 95 97
-97 233 235 96 98
-98 99 234 236 97
-99 100 235 237 98
-100 99 101 236 238
-101 100 102 237 239
-102 101 103 238 240
-103 102 104 239 241
-104 242 103 105 240
-105 243 104 106 241
-106 242 244 105 107
-107 243 245 106 108
-108 244 246 107 109
-109 110 245 247 108
-110 111 246 248 109
-111 110 112 247 249
-112 111 113 248 250
-113 112 114 249 251
-114 113 115 250 252
-115 253 114 116 251
-116 254 115 117 252
-117 253 255 116 118
-118 254 256 117 119
-119 255 257 118 120
-120 121 256 258 119
-121 122 257 259 120
-122 121 123 258 260
-123 122 124 259 261
-124 123 125 260 262
-125 124 126 261 263
-126 264 125 127 262
-127 265 126 128 263
-128 264 266 127 129
-129 265 267 128 130
-130 266 268 129 131
-131 132 267 269 130
-132 133 268 270 131
-133 132 134 269 271
-134 133 135 270 272
-135 134 136 271 273
-136 135 137 272 274
-137 1 136 138 273
-138 2 137 139 274
-139 1 3 138 140
-140 2 4 139 141
-141 3 5 140 142
-142 143 4 6 141
-143 144 5 7 142
-144 143 145 6 8
-145 144 146 7 9
-146 145 147 8 10
-147 11 146 148 9
-148 12 147 149 10
-149 11 13 148 150
-150 12 14 149 151
-151 13 15 150 152
-152 14 16 151 153
-153 154 15 17 152
-154 155 16 18 153
-155 154 156 17 19
-156 155 157 18 20
-157 156 158 19 21
-158 22 157 159 20
-159 23 158 160 21
-160 22 24 159 161
-161 23 25 160 162
-162 24 26 161 163
-163 25 27 162 164
-164 165 26 28 163
-165 166 27 29 164
-166 165 167 28 30
-167 166 168 29 31
-168 167 169 30 32
-169 33 168 170 31
-170 34 169 171 32
-171 33 35 170 172
-172 34 36 171 173
-173 35 37 172 174
-174 36 38 173 175
-175 176 37 39 174
-176 177 38 40 175
-177 176 178 39 41
-178 177 179 40 42
-179 178 180 41 43
-180 44 179 181 42
-181 45 180 182 43
-182 44 46 181 183
-183 45 47 182 184
-184 46 48 183 185
-185 47 49 184 186
-186 187 48 50 185
-187 188 49 51 186
-188 187 189 50 52
-189 188 190 51 53
-190 189 191 52 54
-191 55 190 192 53
-192 56 191 193 54
-193 55 57 192 194
-194 56 58 193 195
-195 57 59 194 196
-196 58 60 195 197
-197 198 59 61 196
-198 199 60 62 197
-199 198 200 61 63
-200 199 201 62 64
-201 200 202 63 65
-202 66 201 203 64
-203 67 202 204 65
-204 66 68 203 205
-205 67 69 204 206
-206 68 70 205 207
-207 69 71 206 208
-208 209 70 72 207
-209 210 71 73 208
-210 209 211 72 74
-211 210 212 73 75
-212 211 213 74 76
-213 77 212 214 75
-214 78 213 215 76
-215 77 79 214 216
-216 78 80 215 217
-217 79 81 216 218
-218 80 82 217 219
-219 220 81 83 218
-220 221 82 84 219
-221 220 222 83 85
-222 221 223 84 86
-223 222 224 85 87
-224 88 223 225 86
-225 89 224 226 87
-226 88 90 225 227
-227 89 91 226 228
-228 90 92 227 229
-229 91 93 228 230
-230 231 92 94 229
-231 232 93 95 230
-232 231 233 94 96
-233 232 234 95 97
-234 233 235 96 98
-235 99 234 236 97
-236 100 235 237 98
-237 99 101 236 238
-238 100 102 237 239
-239 101 103 238 240
-240 102 104 239 241
-241 242 103 105 240
-242 243 104 106 241
-243 242 244 105 107
-244 243 245 106 108
-245 244 246 107 109
-246 110 245 247 108
-247 111 246 248 109
-248 110 112 247 249
-249 111 113 248 250
-250 112 114 249 251
-251 113 115 250 252
-252 253 114 116 251
-253 254 115 117 252
-254 253 255 116 118
-255 254 256 117 119
-256 255 257 118 120
-257 121 256 258 119
-258 122 257 259 120
-259 121 123 258 260
-260 122 124 259 261
-261 123 125 260 262
-262 124 126 261 263
-263 264 125 127 262
-264 265 126 128 263
-265 264 266 127 129
-266 265 267 128 130
-267 266 268 129 131
-268 132 267 269 130
-269 133 268 270 131
-270 132 134 269 271
-271 133 135 270 272
-272 134 136 271 273
-273 135 137 272 274
-274 1 136 138 273
0

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