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