C4graphGraph forms for C4 [ 216, 18 ] = R_108(56,55)

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On this page are computer-accessible forms for the graph C4[ 216, 18 ] = R_108(56,55).

(I) Following is a form readable by MAGMA:

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

(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: (42, 149)(43, 97)(44, 205)(96, 203)(98, 151)(150, 204)
b: (18, 125)(19, 73)(20, 181)(72, 179)(74, 127)(126, 180)
c: (36, 143)(37, 91)(38, 199)(90, 197)(92, 145)(144, 198)
d: (6, 113)(7, 61)(8, 169)(60, 167)(62, 115)(114, 168)
e: (48, 155)(49, 103)(50, 211)(102, 209)(104, 157)(156, 210)
f: (14, 121)(15, 69)(16, 177)(68, 175)(70, 123)(122, 176)
g: (40, 147)(41, 95)(42, 203)(94, 201)(96, 149)(148, 202)
h: (30, 137)(31, 85)(32, 193)(84, 191)(86, 139)(138, 192)
m: (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)
n1: (35, 142)(36, 197)(89, 196)(90, 143)
a1: (31, 138)(32, 193)(85, 192)(86, 139)
b1: (9, 116)(10, 171)(63, 170)(64, 117)
c1: (27, 134)(28, 189)(81, 188)(82, 135)
d1: (20, 127)(21, 75)(22, 183)(74, 181)(76, 129)(128, 182)
e1: (47, 154)(48, 209)(101, 208)(102, 155)
f1: (5, 112)(6, 167)(59, 166)(60, 113)
g1: (21, 128)(22, 183)(75, 182)(76, 129)
h1: (16, 123)(17, 71)(18, 179)(70, 177)(72, 125)(124, 178)
m1: (23, 130)(24, 185)(77, 184)(78, 131)
n2: (24, 131)(25, 79)(26, 187)(78, 185)(80, 133)(132, 186)
a2: (39, 146)(40, 201)(93, 200)(94, 147)
b2: (29, 136)(30, 191)(83, 190)(84, 137)
c2: (22, 129)(23, 77)(24, 185)(76, 183)(78, 131)(130, 184)
d2: (32, 139)(33, 87)(34, 195)(86, 193)(88, 141)(140, 194)
e2: (46, 153)(47, 101)(48, 209)(100, 207)(102, 155)(154, 208)
f2: (13, 120)(14, 175)(67, 174)(68, 121)
g2: (45, 152)(46, 207)(99, 206)(100, 153)
h2: (26, 133)(27, 81)(28, 189)(80, 187)(82, 135)(134, 188)
m2: (2, 161)(3, 53)(4, 52)(5, 51)(6, 50)(7, 49)(8, 48)(9, 47)(10, 46)(11, 45)(12, 44)(13, 43)(14, 42)(15, 41)(16, 40)(17, 39)(18, 38)(19, 37)(20, 36)(21, 35)(22, 34)(23, 33)(24, 32)(25, 31)(26, 30)(27, 29)(54, 163)(56, 215)(57, 107)(58, 106)(59, 105)(60, 104)(61, 103)(62, 102)(63, 101)(64, 100)(65, 99)(66, 98)(67, 97)(68, 96)(69, 95)(70, 94)(71, 93)(72, 92)(73, 91)(74, 90)(75, 89)(76, 88)(77, 87)(78, 86)(79, 85)(80, 84)(81, 83)(108, 109)(110, 214)(111, 213)(112, 212)(113, 211)(114, 210)(115, 209)(116, 208)(117, 207)(118, 206)(119, 205)(120, 204)(121, 203)(122, 202)(123, 201)(124, 200)(125, 199)(126, 198)(127, 197)(128, 196)(129, 195)(130, 194)(131, 193)(132, 192)(133, 191)(134, 190)(135, 189)(136, 188)(137, 187)(138, 186)(139, 185)(140, 184)(141, 183)(142, 182)(143, 181)(144, 180)(145, 179)(146, 178)(147, 177)(148, 176)(149, 175)(150, 174)(151, 173)(152, 172)(153, 171)(154, 170)(155, 169)(156, 168)(157, 167)(158, 166)(159, 165)(160, 164)(162, 216)
n3: (4, 111)(5, 59)(6, 167)(58, 165)(60, 113)(112, 166)
a3: (49, 156)(50, 211)(103, 210)(104, 157)
b3: (17, 124)(18, 179)(71, 178)(72, 125)
c3: (53, 160)(54, 215)(107, 214)(108, 161)
d3: (34, 141)(35, 89)(36, 197)(88, 195)(90, 143)(142, 196)
e3: (15, 122)(16, 177)(69, 176)(70, 123)
f3: (52, 159)(53, 107)(54, 215)(106, 213)(108, 161)(160, 214)
g3: (7, 114)(8, 169)(61, 168)(62, 115)
h3: (25, 132)(26, 187)(79, 186)(80, 133)
m3: (19, 126)(20, 181)(73, 180)(74, 127)
n4: (50, 157)(51, 105)(52, 213)(104, 211)(106, 159)(158, 212)
a4: (41, 148)(42, 203)(95, 202)(96, 149)
b4: (38, 145)(39, 93)(40, 201)(92, 199)(94, 147)(146, 200)
c4: (10, 117)(11, 65)(12, 173)(64, 171)(66, 119)(118, 172)
d4: (28, 135)(29, 83)(30, 191)(82, 189)(84, 137)(136, 190)
e4: (51, 158)(52, 213)(105, 212)(106, 159)
f4: (37, 144)(38, 199)(91, 198)(92, 145)
g4: (44, 151)(45, 99)(46, 207)(98, 205)(100, 153)(152, 206)
h4: (33, 140)(34, 195)(87, 194)(88, 141)
m4: (8, 115)(9, 63)(10, 171)(62, 169)(64, 117)(116, 170)
n5: (12, 119)(13, 67)(14, 175)(66, 173)(68, 121)(120, 174)
a5: (11, 118)(12, 173)(65, 172)(66, 119)
b5: (43, 150)(44, 205)(97, 204)(98, 151)

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

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