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On this page are computer-accessible forms for the graph C4[ 256, 1 ] = W(128,2).

(I) Following is a form readable by MAGMA:

g:=Graph<256|{ {2, 3}, {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}, {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}, {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}, {1, 2}, {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}, {49, 50}, {5, 6}, {9, 10}, {13, 14}, {17, 18}, {21, 22}, {25, 26}, {29, 30}, {33, 34}, {37, 38}, {41, 42}, {45, 46}, {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}, {251, 252}, {243, 244}, {235, 236}, {227, 228}, {219, 220}, {211, 212}, {203, 204}, {195, 196}, {187, 188}, {179, 180}, {171, 172}, {75, 76}, {67, 68}, {59, 60}, {51, 52}, {11, 12}, {19, 20}, {27, 28}, {35, 36}, {43, 44}, {83, 84}, {91, 92}, {99, 100}, {107, 108}, {115, 116}, {123, 124}, {131, 132}, {139, 140}, {147, 148}, {155, 156}, {163, 164}, {7, 8}, {247, 248}, {231, 232}, {215, 216}, {199, 200}, {183, 184}, {71, 72}, {55, 56}, {23, 24}, {39, 40}, {87, 88}, {103, 104}, {119, 120}, {135, 136}, {151, 152}, {167, 168}, {15, 16}, {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}, {128, 255}, {1, 128}, {81, 208}, {80, 209}, {79, 206}, {78, 207}, {77, 204}, {76, 205}, {75, 202}, {74, 203}, {73, 200}, {72, 201}, {71, 198}, {70, 199}, {69, 196}, {68, 197}, {67, 194}, {66, 195}, {65, 192}, {64, 193}, {63, 190}, {62, 191}, {61, 188}, {60, 189}, {59, 186}, {58, 187}, {57, 184}, {56, 185}, {55, 182}, {54, 183}, {53, 180}, {52, 181}, {51, 178}, {50, 179}, {49, 176}, {48, 177}, {2, 131}, {3, 130}, {4, 133}, {5, 132}, {6, 135}, {7, 134}, {8, 137}, {9, 136}, {10, 139}, {11, 138}, {12, 141}, {13, 140}, {14, 143}, {15, 142}, {16, 145}, {17, 144}, {18, 147}, {19, 146}, {20, 149}, {21, 148}, {22, 151}, {23, 150}, {24, 153}, {25, 152}, {26, 155}, {27, 154}, {28, 157}, {29, 156}, {30, 159}, {31, 158}, {32, 161}, {33, 160}, {34, 163}, {35, 162}, {36, 165}, {37, 164}, {38, 167}, {39, 166}, {40, 169}, {41, 168}, {42, 171}, {43, 170}, {44, 173}, {45, 172}, {46, 175}, {47, 174}, {82, 211}, {83, 210}, {84, 213}, {85, 212}, {86, 215}, {87, 214}, {88, 217}, {89, 216}, {90, 219}, {91, 218}, {92, 221}, {93, 220}, {94, 223}, {95, 222}, {96, 225}, {97, 224}, {98, 227}, {99, 226}, {100, 229}, {101, 228}, {102, 231}, {103, 230}, {104, 233}, {105, 232}, {106, 235}, {107, 234}, {108, 237}, {109, 236}, {110, 239}, {111, 238}, {112, 241}, {113, 240}, {114, 243}, {115, 242}, {116, 245}, {117, 244}, {118, 247}, {119, 246}, {120, 249}, {121, 248}, {122, 251}, {123, 250}, {124, 253}, {125, 252}, {126, 255}, {127, 254}, {1, 130}, {81, 210}, {78, 205}, {77, 206}, {74, 201}, {73, 202}, {70, 197}, {69, 198}, {66, 193}, {65, 194}, {62, 189}, {61, 190}, {58, 185}, {57, 186}, {54, 181}, {53, 182}, {50, 177}, {49, 178}, {2, 129}, {5, 134}, {6, 133}, {9, 138}, {10, 137}, {13, 142}, {14, 141}, {17, 146}, {18, 145}, {21, 150}, {22, 149}, {25, 154}, {26, 153}, {29, 158}, {30, 157}, {33, 162}, {34, 161}, {37, 166}, {38, 165}, {41, 170}, {42, 169}, {45, 174}, {46, 173}, {82, 209}, {85, 214}, {86, 213}, {89, 218}, {90, 217}, {93, 222}, {94, 221}, {97, 226}, {98, 225}, {101, 230}, {102, 229}, {105, 234}, {106, 233}, {109, 238}, {110, 237}, {113, 242}, {114, 241}, {117, 246}, {118, 245}, {121, 250}, {122, 249}, {125, 254}, {126, 253}, {3, 132}, {76, 203}, {75, 204}, {68, 195}, {67, 196}, {60, 187}, {59, 188}, {52, 179}, {51, 180}, {4, 131}, {11, 140}, {12, 139}, {19, 148}, {20, 147}, {27, 156}, {28, 155}, {35, 164}, {36, 163}, {43, 172}, {44, 171}, {83, 212}, {84, 211}, {91, 220}, {92, 219}, {99, 228}, {100, 227}, {107, 236}, {108, 235}, {115, 244}, {116, 243}, {123, 252}, {124, 251}, {7, 136}, {72, 199}, {71, 200}, {56, 183}, {55, 184}, {8, 135}, {23, 152}, {24, 151}, {39, 168}, {40, 167}, {87, 216}, {88, 215}, {103, 232}, {104, 231}, {119, 248}, {120, 247}, {15, 144}, {80, 207}, {79, 208}, {48, 175}, {16, 143}, {47, 176}, {111, 240}, {112, 239}, {31, 160}, {32, 159}, {95, 224}, {96, 223}, {63, 192}, {64, 191}, {127, 128}, {1, 256}, {127, 256}, {129, 256}, {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: (127, 255)
b: (78, 206)
c: (51, 179)
d: (79, 207)
e: (50, 178)
f: (80, 208)
g: (49, 177)
h: (81, 209)
m: (48, 176)
n1: (82, 210)
a1: (47, 175)
b1: (83, 211)
c1: (46, 174)
d1: (84, 212)
e1: (45, 173)
f1: (85, 213)
g1: (44, 172)
h1: (86, 214)
m1: (43, 171)
n2: (87, 215)
a2: (42, 170)
b2: (88, 216)
c2: (41, 169)
d2: (89, 217)
e2: (40, 168)
f2: (90, 218)
g2: (39, 167)
h2: (91, 219)
m2: (38, 166)
n3: (92, 220)
a3: (37, 165)
b3: (93, 221)
c3: (36, 164)
d3: (94, 222)
e3: (35, 163)
f3: (95, 223)
g3: (34, 162)
h3: (96, 224)
m3: (33, 161)
n4: (97, 225)
a4: (32, 160)
b4: (98, 226)
c4: (31, 159)
d4: (99, 227)
e4: (18, 146)
f4: (112, 240)
g4: (17, 145)
h4: (113, 241)
m4: (16, 144)
n5: (114, 242)
a5: (15, 143)
b5: (115, 243)
c5: (14, 142)
d5: (116, 244)
e5: (13, 141)
f5: (117, 245)
g5: (12, 140)
h5: (118, 246)
m5: (11, 139)
n6: (119, 247)
a6: (10, 138)
b6: (120, 248)
c6: (9, 137)
d6: (121, 249)
e6: (8, 136)
f6: (122, 250)
g6: (7, 135)
h6: (123, 251)
m6: (6, 134)
n7: (124, 252)
a7: (5, 133)
b7: (125, 253)
c7: (4, 132)
d7: (126, 254)
e7: (3, 131)
f7: (111, 239)
g7: (19, 147)
h7: (110, 238)
m7: (20, 148)
n8: (109, 237)
a8: (21, 149)
b8: (108, 236)
c8: (22, 150)
d8: (107, 235)
e8: (23, 151)
f8: (106, 234)
g8: (24, 152)
h8: (105, 233)
m8: (25, 153)
n9: (104, 232)
a9: (26, 154)
b9: (103, 231)
c9: (27, 155)
d9: (102, 230)
e9: (28, 156)
f9: (101, 229)
g9: (29, 157)
h9: (100, 228)
m9: (30, 158)
n10: (52, 180)
a10: (77, 205)
b10: (53, 181)
c10: (76, 204)
d10: (54, 182)
e10: (75, 203)
f10: (55, 183)
g10: (74, 202)
h10: (56, 184)
m10: (73, 201)
n11: (57, 185)
a11: (72, 200)
b11: (58, 186)
c11: (71, 199)
d11: (59, 187)
e11: (70, 198)
f11: (60, 188)
g11: (69, 197)
h11: (61, 189)
m11: (68, 196)
n12: (62, 190)
a12: (67, 195)
b12: (66, 194)
c12: (64, 192)
d12: (65, 193)
e12: (128, 256)
f12: (2, 130)
g12: (2, 128)(3, 127)(4, 126)(5, 125)(6, 124)(7, 123)(8, 122)(9, 121)(10, 120)(11, 119)(12, 118)(13, 117)(14, 116)(15, 115)(16, 114)(17, 113)(18, 112)(19, 111)(20, 110)(21, 109)(22, 108)(23, 107)(24, 106)(25, 105)(26, 104)(27, 103)(28, 102)(29, 101)(30, 100)(31, 99)(32, 98)(33, 97)(34, 96)(35, 95)(36, 94)(37, 93)(38, 92)(39, 91)(40, 90)(41, 89)(42, 88)(43, 87)(44, 86)(45, 85)(46, 84)(47, 83)(48, 82)(49, 81)(50, 80)(51, 79)(52, 78)(53, 77)(54, 76)(55, 75)(56, 74)(57, 73)(58, 72)(59, 71)(60, 70)(61, 69)(62, 68)(63, 67)(64, 66)(130, 256)(131, 255)(132, 254)(133, 253)(134, 252)(135, 251)(136, 250)(137, 249)(138, 248)(139, 247)(140, 246)(141, 245)(142, 244)(143, 243)(144, 242)(145, 241)(146, 240)(147, 239)(148, 238)(149, 237)(150, 236)(151, 235)(152, 234)(153, 233)(154, 232)(155, 231)(156, 230)(157, 229)(158, 228)(159, 227)(160, 226)(161, 225)(162, 224)(163, 223)(164, 222)(165, 221)(166, 220)(167, 219)(168, 218)(169, 217)(170, 216)(171, 215)(172, 214)(173, 213)(174, 212)(175, 211)(176, 210)(177, 209)(178, 208)(179, 207)(180, 206)(181, 205)(182, 204)(183, 203)(184, 202)(185, 201)(186, 200)(187, 199)(188, 198)(189, 197)(190, 196)(191, 195)(192, 194)
h12: (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)

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

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