Graph forms
for C4 [ 210, 6 ] = PS(30,7;2)
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On this page are computer-accessible forms for the graph C4[ 210, 6 ] =
PS(30,7;2).
(I) Following is a form readable by MAGMA:
g:=Graph<210|{ {28, 29}, {196, 197}, {70, 71}, {112, 113}, {154, 155}, {13, 15},
{181, 183}, {97, 99}, {77, 79}, {76, 78}, {56, 58}, {140, 142}, {160, 162},
{161, 163}, {20, 23}, {188, 191}, {104, 107}, {84, 87}, {40, 43}, {49, 50},
{124, 127}, {133, 134}, {168, 171}, {18, 22}, {187, 191}, {186, 190}, {105,
109}, {104, 108}, {83, 87}, {82, 86}, {81, 85}, {19, 23}, {40, 44}, {41, 45},
{42, 46}, {123, 127}, {144, 148}, {145, 149}, {146, 150}, {147, 151}, {168,
172}, {10, 15}, {202, 207}, {200, 205}, {187, 190}, {178, 183}, {105, 108}, {98,
103}, {96, 101}, {83, 86}, {74, 79}, {19, 22}, {32, 37}, {34, 39}, {41, 44},
{56, 61}, {136, 141}, {138, 143}, {145, 148}, {147, 150}, {160, 165}, {24, 30},
{203, 205}, {202, 204}, {193, 199}, {192, 198}, {98, 100}, {89, 95}, {88, 94},
{25, 31}, {34, 36}, {35, 37}, {48, 54}, {49, 55}, {65, 71}, {112, 118}, {128,
134}, {129, 135}, {139, 141}, {152, 158}, {153, 159}, {33, 38}, {201, 206}, {97,
102}, {91, 92}, {82, 85}, {73, 78}, {42, 45}, {137, 142}, {146, 149}, {161,
166}, {1, 9}, {195, 203}, {194, 202}, {193, 201}, {192, 200}, {87, 95}, {86,
94}, {85, 93}, {69, 77}, {68, 76}, {67, 75}, {2, 10}, {3, 11}, {4, 12}, {5, 13},
{6, 14}, {22, 30}, {23, 31}, {48, 56}, {64, 72}, {65, 73}, {66, 74}, {128, 136},
{129, 137}, {130, 138}, {131, 139}, {132, 140}, {148, 156}, {149, 157}, {150,
158}, {151, 159}, {32, 41}, {198, 207}, {180, 189}, {178, 187}, {96, 105}, {50,
59}, {52, 61}, {54, 63}, {114, 123}, {116, 125}, {134, 143}, {176, 185}, {2, 8},
{195, 201}, {194, 200}, {101, 111}, {100, 110}, {87, 93}, {86, 92}, {81, 91},
{80, 90}, {70, 76}, {67, 73}, {3, 9}, {6, 12}, {7, 13}, {16, 26}, {17, 27}, {23,
29}, {36, 46}, {37, 47}, {66, 72}, {130, 136}, {131, 137}, {144, 154}, {150,
156}, {151, 157}, {164, 174}, {165, 175}, {16, 27}, {199, 204}, {197, 206},
{179, 184}, {100, 111}, {80, 91}, {33, 42}, {35, 40}, {36, 47}, {53, 62}, {55,
60}, {113, 122}, {115, 120}, {117, 126}, {119, 124}, {164, 175}, {177, 186},
{20, 24}, {103, 107}, {102, 106}, {84, 88}, {21, 25}, {39, 43}, {50, 62}, {51,
63}, {113, 125}, {114, 126}, {165, 169}, {166, 170}, {167, 171}, {176, 188},
{177, 189}, {17, 28}, {182, 187}, {180, 185}, {103, 106}, {99, 110}, {21, 24},
{52, 57}, {54, 59}, {64, 77}, {116, 121}, {118, 123}, {163, 174}, {167, 170},
{4, 10}, {196, 202}, {182, 184}, {99, 109}, {69, 75}, {68, 74}, {5, 11}, {18,
28}, {55, 57}, {118, 120}, {119, 121}, {132, 138}, {133, 139}, {149, 155}, {162,
172}, {163, 173}, {1, 14}, {181, 186}, {179, 188}, {7, 8}, {51, 60}, {53, 58},
{115, 124}, {117, 122}, {162, 173}, {166, 169}, {43, 56}, {71, 83}, {198, 210},
{197, 209}, {134, 146}, {135, 147}, {15, 26}, {101, 112}, {79, 90}, {37, 48},
{141, 152}, {143, 154}, {15, 25}, {102, 112}, {79, 89}, {78, 88}, {38, 48}, {39,
49}, {142, 152}, {143, 153}, {38, 49}, {199, 208}, {78, 89}, {71, 80}, {135,
144}, {142, 153}, {43, 51}, {106, 114}, {44, 52}, {45, 53}, {46, 54}, {47, 55},
{107, 115}, {108, 116}, {109, 117}, {110, 118}, {111, 119}, {169, 177}, {170,
178}, {171, 179}, {172, 180}, {173, 181}, {174, 182}, {8, 17}, {200, 209}, {74,
83}, {72, 81}, {10, 19}, {12, 21}, {136, 145}, {138, 147}, {46, 52}, {47, 53},
{107, 113}, {110, 116}, {111, 117}, {141, 151}, {170, 176}, {171, 177}, {174,
180}, {175, 181}, {9, 18}, {203, 208}, {201, 210}, {75, 80}, {73, 82}, {11, 16},
{137, 146}, {139, 144}, {8, 20}, {72, 84}, {9, 21}, {12, 17}, {76, 81}, {14,
19}, {106, 119}, {140, 145}, {14, 16}, {44, 50}, {45, 51}, {108, 114}, {109,
115}, {172, 178}, {173, 179}, {11, 20}, {77, 82}, {75, 84}, {13, 18}, {169,
182}, {175, 176}, {29, 41}, {93, 105}, {92, 104}, {30, 42}, {156, 168}, {22,
35}, {148, 161}, {31, 40}, {95, 104}, {85, 98}, {159, 168}, {24, 32}, {90, 98},
{89, 97}, {88, 96}, {25, 33}, {26, 34}, {27, 35}, {152, 160}, {153, 161}, {30,
39}, {94, 103}, {92, 101}, {156, 165}, {158, 167}, {26, 32}, {91, 97}, {90, 96},
{27, 33}, {154, 160}, {29, 38}, {95, 100}, {93, 102}, {31, 36}, {157, 166},
{159, 164}, {155, 167}, {94, 99}, {158, 163}, {28, 34}, {155, 164}, {157, 162},
{183, 194}, {190, 203}, {183, 193}, {190, 198}, {191, 199}, {57, 67}, {191,
197}, {185, 195}, {184, 194}, {60, 70}, {184, 195}, {60, 64}, {189, 193}, {188,
192}, {61, 65}, {62, 66}, {63, 67}, {57, 68}, {189, 192}, {185, 196}, {59, 70},
{61, 64}, {63, 66}, {58, 68}, {186, 196}, {59, 69}, {58, 69}, {62, 65}, {4,
204}, {5, 205}, {6, 206}, {7, 207}, {5, 204}, {7, 206}, {6, 205}, {1, 207}, {1,
208}, {3, 210}, {2, 208}, {3, 209}, {2, 209}, {4, 210}, {127, 140}, {127, 135},
{120, 130}, {121, 131}, {120, 131}, {124, 128}, {125, 129}, {126, 130}, {121,
132}, {125, 128}, {122, 132}, {123, 133}, {122, 133}, {126, 129} }>;
(II) A more general form is to represent the graph as the orbit of {28, 29}
under the group generated by the following permutations:
a: (1, 2)(3, 7)(4, 6)(8, 9)(10, 14)(11, 13)(15, 16)(17, 21)(18, 20)(22, 23)(24,
28)(25, 27)(29, 30)(31, 35)(32, 34)(36, 37)(38, 42)(39, 41)(43, 44)(45, 49)(46,
48)(50, 51)(52, 56)(53, 55)(57, 58)(59, 63)(60, 62)(64, 65)(66, 70)(67, 69)(71,
72)(73, 77)(74, 76)(78, 79)(80, 84)(81, 83)(85, 86)(87, 91)(88, 90)(92, 93)(94,
98)(95, 97)(99, 100)(101, 105)(102, 104)(106, 107)(108, 112)(109, 111)(113,
114)(115, 119)(116, 118)(120, 121)(122, 126)(123, 125)(127, 128)(129, 133)(130,
132)(134, 135)(136, 140)(137, 139)(141, 142)(143, 147)(144, 146)(148, 149)(150,
154)(151, 153)(155, 156)(157, 161)(158, 160)(162, 163)(164, 168)(165, 167)(169,
170)(171, 175)(172, 174)(176, 177)(178, 182)(179, 181)(183, 184)(185, 189)(186,
188)(190, 191)(192, 196)(193, 195)(197, 198)(199, 203)(200, 202)(204, 205)(206,
210)(207, 209) (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 **************
b: (1, 8, 15, 22, 29, 36, 43, 50, 57, 64, 71, 78, 85, 92, 99, 106, 113, 120,
127, 134, 141, 148, 155, 162, 169, 176, 183, 190, 197, 204)(2, 10, 19, 23, 31,
40, 44, 52, 61, 65, 73, 82, 86, 94, 103, 107, 115, 124, 128, 136, 145, 149, 157,
166, 170, 178, 187, 191, 199, 208)(3, 12, 16, 24, 33, 37, 45, 54, 58, 66, 75,
79, 87, 96, 100, 108, 117, 121, 129, 138, 142, 150, 159, 163, 171, 180, 184,
192, 201, 205)(4, 14, 20, 25, 35, 41, 46, 56, 62, 67, 77, 83, 88, 98, 104, 109,
119, 125, 130, 140, 146, 151, 161, 167, 172, 182, 188, 193, 203, 209)(5, 9, 17,
26, 30, 38, 47, 51, 59, 68, 72, 80, 89, 93, 101, 110, 114, 122, 131, 135, 143,
152, 156, 164, 173, 177, 185, 194, 198, 206)(6, 11, 21, 27, 32, 42, 48, 53, 63,
69, 74, 84, 90, 95, 105, 111, 116, 126, 132, 137, 147, 153, 158, 168, 174, 179,
189, 195, 200, 210)(7, 13, 18, 28, 34, 39, 49, 55, 60, 70, 76, 81, 91, 97, 102,
112, 118, 123, 133, 139, 144, 154, 160, 165, 175, 181, 186, 196, 202, 207)
c: (2, 7)(3, 6)(4, 5)(9, 14)(10, 13)(11, 12)(16, 21)(17, 20)(18, 19)(23, 28)(24,
27)(25, 26)(30, 35)(31, 34)(32, 33)(37, 42)(38, 41)(39, 40)(44, 49)(45, 48)(46,
47)(51, 56)(52, 55)(53, 54)(58, 63)(59, 62)(60, 61)(65, 70)(66, 69)(67, 68)(72,
77)(73, 76)(74, 75)(79, 84)(80, 83)(81, 82)(86, 91)(87, 90)(88, 89)(93, 98)(94,
97)(95, 96)(100, 105)(101, 104)(102, 103)(107, 112)(108, 111)(109, 110)(114,
119)(115, 118)(116, 117)(121, 126)(122, 125)(123, 124)(128, 133)(129, 132)(130,
131)(135, 140)(136, 139)(137, 138)(142, 147)(143, 146)(144, 145)(149, 154)(150,
153)(151, 152)(156, 161)(157, 160)(158, 159)(163, 168)(164, 167)(165, 166)(170,
175)(171, 174)(172, 173)(177, 182)(178, 181)(179, 180)(184, 189)(185, 188)(186,
187)(191, 196)(192, 195)(193, 194)(198, 203)(199, 202)(200, 201)(205, 210)(206,
209)(207, 208)
C4[ 210, 6 ]
210
-1 14 9 207 208
-2 209 8 10 208
-3 11 209 210 9
-4 12 210 204 10
-5 11 13 204 205
-6 12 14 205 206
-7 13 8 206 207
-8 2 17 7 20
-9 1 3 18 21
-10 2 4 15 19
-11 3 5 16 20
-12 4 6 17 21
-13 15 5 7 18
-14 1 16 6 19
-15 13 25 26 10
-16 11 14 26 27
-17 12 27 28 8
-18 22 13 28 9
-19 22 23 14 10
-20 11 23 24 8
-21 12 24 25 9
-22 35 18 19 30
-23 29 19 20 31
-24 30 20 21 32
-25 33 15 31 21
-26 34 15 16 32
-27 33 35 16 17
-28 34 17 18 29
-29 23 38 28 41
-30 22 24 39 42
-31 23 25 36 40
-32 24 26 37 41
-33 25 27 38 42
-34 36 26 28 39
-35 22 37 27 40
-36 34 46 47 31
-37 35 47 48 32
-38 33 48 49 29
-39 34 49 30 43
-40 44 35 31 43
-41 44 45 29 32
-42 33 45 46 30
-43 56 39 40 51
-44 50 40 41 52
-45 51 41 42 53
-46 36 52 42 54
-47 55 36 37 53
-48 56 37 38 54
-49 55 38 39 50
-50 44 59 49 62
-51 45 60 63 43
-52 44 46 57 61
-53 45 47 58 62
-54 46 48 59 63
-55 57 47 49 60
-56 58 48 61 43
-57 55 67 68 52
-58 56 68 69 53
-59 69 70 50 54
-60 55 70 51 64
-61 56 52 64 65
-62 66 50 53 65
-63 66 67 51 54
-64 77 60 61 72
-65 71 61 62 73
-66 72 62 63 74
-67 57 73 63 75
-68 57 58 74 76
-69 77 58 59 75
-70 59 60 71 76
-71 80 70 83 65
-72 66 81 84 64
-73 67 78 82 65
-74 66 68 79 83
-75 67 69 80 84
-76 78 68 70 81
-77 79 69 82 64
-78 88 89 73 76
-79 77 89 90 74
-80 90 91 71 75
-81 91 72 85 76
-82 77 73 85 86
-83 71 74 86 87
-84 88 72 75 87
-85 81 82 93 98
-86 92 82 83 94
-87 93 83 84 95
-88 78 94 84 96
-89 78 79 95 97
-90 79 80 96 98
-91 80 81 92 97
-92 101 91 104 86
-93 102 105 85 87
-94 88 99 103 86
-95 89 100 104 87
-96 88 90 101 105
-97 99 89 91 102
-98 100 90 103 85
-99 110 94 97 109
-100 110 111 95 98
-101 111 112 92 96
-102 112 93 106 97
-103 94 106 107 98
-104 92 95 107 108
-105 93 96 108 109
-106 102 103 114 119
-107 113 103 104 115
-108 114 104 105 116
-109 99 115 105 117
-110 99 100 116 118
-111 100 101 117 119
-112 101 102 113 118
-113 122 112 125 107
-114 123 126 106 108
-115 124 107 109 120
-116 110 121 125 108
-117 111 122 126 109
-118 110 112 123 120
-119 121 111 124 106
-120 115 118 130 131
-121 132 116 119 131
-122 132 133 113 117
-123 133 114 127 118
-124 115 127 128 119
-125 113 116 128 129
-126 114 117 129 130
-127 123 124 135 140
-128 134 124 125 136
-129 135 125 126 137
-130 136 126 138 120
-131 121 137 139 120
-132 121 122 138 140
-133 122 123 134 139
-134 143 133 146 128
-135 144 147 127 129
-136 145 128 130 141
-137 146 129 131 142
-138 132 143 147 130
-139 133 144 141 131
-140 132 145 127 142
-141 136 139 151 152
-142 137 140 152 153
-143 154 134 138 153
-144 154 135 148 139
-145 136 148 149 140
-146 134 137 149 150
-147 135 138 150 151
-148 144 145 156 161
-149 155 145 146 157
-150 156 146 147 158
-151 157 147 159 141
-152 158 160 141 142
-153 143 159 161 142
-154 143 144 155 160
-155 154 167 149 164
-156 165 168 148 150
-157 166 149 151 162
-158 167 150 152 163
-159 168 151 153 164
-160 154 165 162 152
-161 166 148 163 153
-162 157 160 172 173
-163 158 161 173 174
-164 155 159 174 175
-165 156 169 160 175
-166 157 169 170 161
-167 155 158 170 171
-168 156 159 171 172
-169 165 166 177 182
-170 176 166 167 178
-171 177 167 168 179
-172 178 168 180 162
-173 179 181 162 163
-174 180 182 163 164
-175 165 176 181 164
-176 188 170 185 175
-177 189 169 171 186
-178 187 170 172 183
-179 188 171 173 184
-180 189 172 174 185
-181 183 173 175 186
-182 187 169 184 174
-183 178 181 193 194
-184 179 182 194 195
-185 176 180 195 196
-186 177 190 181 196
-187 178 190 191 182
-188 176 179 191 192
-189 177 180 192 193
-190 187 198 203 186
-191 187 188 199 197
-192 198 188 189 200
-193 199 189 201 183
-194 200 202 183 184
-195 201 203 184 185
-196 202 185 186 197
-197 209 191 206 196
-198 210 190 192 207
-199 191 193 204 208
-200 209 192 194 205
-201 210 193 195 206
-202 204 194 196 207
-203 190 205 195 208
-204 199 4 202 5
-205 200 5 203 6
-206 201 6 7 197
-207 198 1 202 7
-208 1 199 2 203
-209 2 200 3 197
-210 198 3 201 4
0