Graph forms
for C4 [ 250, 5 ] = PS(50,5;2)
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On this page are computer-accessible forms for the graph C4[ 250, 5 ] =
PS(50,5;2).
(I) Following is a form readable by MAGMA:
g:=Graph<250|{ {9, 11}, {240, 242}, {229, 231}, {129, 131}, {120, 122}, {109,
111}, {100, 102}, {89, 91}, {20, 22}, {29, 31}, {40, 42}, {49, 51}, {60, 62},
{69, 71}, {80, 82}, {140, 142}, {149, 151}, {160, 162}, {169, 171}, {180, 182},
{189, 191}, {200, 202}, {209, 211}, {220, 222}, {5, 6}, {245, 246}, {240, 243},
{228, 231}, {225, 226}, {128, 131}, {125, 126}, {120, 123}, {108, 111}, {105,
106}, {100, 103}, {88, 91}, {85, 86}, {8, 11}, {20, 23}, {25, 26}, {28, 31},
{40, 43}, {45, 46}, {48, 51}, {60, 63}, {65, 66}, {68, 71}, {80, 83}, {140,
143}, {145, 146}, {148, 151}, {160, 163}, {165, 166}, {168, 171}, {180, 183},
{185, 186}, {188, 191}, {200, 203}, {205, 206}, {208, 211}, {220, 223}, {2, 6},
{243, 247}, {242, 246}, {235, 239}, {234, 238}, {233, 237}, {232, 236}, {225,
229}, {123, 127}, {122, 126}, {115, 119}, {114, 118}, {113, 117}, {112, 116},
{105, 109}, {104, 108}, {83, 87}, {3, 7}, {24, 28}, {25, 29}, {32, 36}, {33,
37}, {34, 38}, {35, 39}, {42, 46}, {43, 47}, {64, 68}, {65, 69}, {72, 76}, {73,
77}, {74, 78}, {75, 79}, {82, 86}, {144, 148}, {145, 149}, {152, 156}, {153,
157}, {154, 158}, {155, 159}, {162, 166}, {163, 167}, {184, 188}, {185, 189},
{192, 196}, {193, 197}, {194, 198}, {195, 199}, {202, 206}, {203, 207}, {224,
228}, {9, 12}, {129, 132}, {99, 102}, {89, 92}, {19, 22}, {49, 52}, {59, 62},
{139, 142}, {169, 172}, {179, 182}, {209, 212}, {219, 222}, {1, 7}, {241, 247},
{233, 239}, {232, 238}, {130, 132}, {121, 127}, {113, 119}, {112, 118}, {104,
110}, {99, 101}, {90, 92}, {10, 12}, {19, 21}, {24, 30}, {32, 38}, {33, 39},
{41, 47}, {50, 52}, {59, 61}, {64, 70}, {72, 78}, {73, 79}, {81, 87}, {139,
141}, {144, 150}, {152, 158}, {153, 159}, {161, 167}, {170, 172}, {179, 181},
{184, 190}, {192, 198}, {193, 199}, {201, 207}, {210, 212}, {219, 221}, {224,
230}, {8, 15}, {235, 236}, {130, 133}, {128, 135}, {115, 116}, {98, 101}, {96,
103}, {90, 93}, {88, 95}, {10, 13}, {16, 23}, {18, 21}, {35, 36}, {48, 55}, {50,
53}, {56, 63}, {58, 61}, {75, 76}, {136, 143}, {138, 141}, {155, 156}, {168,
175}, {170, 173}, {176, 183}, {178, 181}, {195, 196}, {208, 215}, {210, 213},
{216, 223}, {218, 221}, {6, 14}, {227, 235}, {226, 234}, {117, 125}, {116, 124},
{97, 105}, {96, 104}, {87, 95}, {86, 94}, {7, 15}, {16, 24}, {17, 25}, {36, 44},
{37, 45}, {66, 74}, {67, 75}, {146, 154}, {147, 155}, {166, 174}, {167, 175},
{176, 184}, {177, 185}, {196, 204}, {197, 205}, {7, 14}, {227, 234}, {117, 124},
{97, 104}, {87, 94}, {17, 24}, {37, 44}, {67, 74}, {147, 154}, {167, 174}, {177,
184}, {197, 204}, {2, 8}, {243, 249}, {242, 248}, {231, 237}, {134, 140}, {131,
137}, {114, 120}, {103, 109}, {102, 108}, {83, 89}, {3, 9}, {22, 28}, {23, 29},
{34, 40}, {51, 57}, {54, 60}, {71, 77}, {82, 88}, {151, 157}, {162, 168}, {163,
169}, {182, 188}, {183, 189}, {194, 200}, {211, 217}, {214, 220}, {1, 10}, {241,
250}, {226, 233}, {118, 125}, {101, 110}, {98, 105}, {86, 93}, {6, 13}, {18,
25}, {21, 30}, {38, 45}, {66, 73}, {81, 90}, {146, 153}, {161, 170}, {166, 173},
{178, 185}, {181, 190}, {198, 205}, {4, 8}, {245, 249}, {244, 248}, {134, 138},
{133, 137}, {132, 136}, {103, 107}, {102, 106}, {85, 89}, {84, 88}, {5, 9}, {22,
26}, {23, 27}, {52, 56}, {53, 57}, {54, 58}, {55, 59}, {135, 139}, {164, 168},
{165, 169}, {182, 186}, {183, 187}, {212, 216}, {213, 217}, {214, 218}, {215,
219}, {39, 42}, {229, 232}, {119, 122}, {69, 72}, {149, 152}, {199, 202}, {4,
10}, {244, 250}, {230, 232}, {133, 139}, {132, 138}, {119, 121}, {101, 107},
{84, 90}, {21, 27}, {39, 41}, {52, 58}, {53, 59}, {70, 72}, {150, 152}, {164,
170}, {181, 187}, {199, 201}, {212, 218}, {213, 219}, {36, 43}, {230, 233},
{228, 235}, {131, 140}, {118, 121}, {116, 123}, {38, 41}, {51, 60}, {55, 56},
{68, 75}, {70, 73}, {135, 136}, {148, 155}, {150, 153}, {196, 203}, {198, 201},
{211, 220}, {215, 216}, {71, 80}, {231, 240}, {111, 120}, {46, 54}, {237, 245},
{236, 244}, {107, 115}, {106, 114}, {47, 55}, {76, 84}, {77, 85}, {136, 144},
{137, 145}, {206, 214}, {207, 215}, {47, 54}, {237, 244}, {107, 114}, {77, 84},
{137, 144}, {207, 214}, {11, 17}, {234, 240}, {111, 117}, {14, 20}, {42, 48},
{43, 49}, {74, 80}, {142, 148}, {143, 149}, {171, 177}, {174, 180}, {202, 208},
{203, 209}, {41, 50}, {238, 245}, {106, 113}, {46, 53}, {78, 85}, {138, 145},
{141, 150}, {201, 210}, {206, 213}, {12, 16}, {13, 17}, {14, 18}, {15, 19}, {44,
48}, {45, 49}, {142, 146}, {143, 147}, {172, 176}, {173, 177}, {174, 178}, {175,
179}, {204, 208}, {205, 209}, {79, 82}, {239, 242}, {109, 112}, {12, 18}, {239,
241}, {110, 112}, {13, 19}, {44, 50}, {79, 81}, {141, 147}, {172, 178}, {173,
179}, {204, 210}, {11, 20}, {238, 241}, {236, 243}, {110, 113}, {108, 115}, {15,
16}, {76, 83}, {78, 81}, {171, 180}, {175, 176}, {31, 40}, {151, 160}, {26, 34},
{27, 35}, {156, 164}, {157, 165}, {216, 224}, {217, 225}, {27, 34}, {157, 164},
{217, 224}, {31, 37}, {94, 100}, {91, 97}, {154, 160}, {222, 228}, {223, 229},
{26, 33}, {158, 165}, {218, 225}, {221, 230}, {92, 96}, {95, 99}, {94, 98}, {93,
97}, {222, 226}, {223, 227}, {29, 32}, {159, 162}, {30, 32}, {93, 99}, {92, 98},
{159, 161}, {221, 227}, {28, 35}, {95, 96}, {91, 100}, {30, 33}, {156, 163},
{158, 161}, {191, 200}, {56, 64}, {57, 65}, {186, 194}, {187, 195}, {57, 64},
{187, 194}, {62, 68}, {63, 69}, {191, 197}, {58, 65}, {61, 70}, {186, 193}, {62,
66}, {63, 67}, {189, 192}, {61, 67}, {190, 192}, {188, 195}, {190, 193}, {4,
246}, {5, 247}, {4, 247}, {3, 246}, {1, 249}, {127, 135}, {126, 134}, {2, 250},
{1, 248}, {127, 134}, {3, 250}, {122, 128}, {123, 129}, {2, 249}, {126, 133},
{121, 130}, {124, 128}, {125, 129}, {5, 248}, {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, 211, 216, 221, 226, 231, 236, 241, 246)(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, 215, 219, 222, 228, 235, 239, 242, 248, 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, 212, 218, 225, 229, 232, 238, 245, 249)(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, 214, 217, 223, 230, 234, 237, 243, 250, 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, 213,
220, 224, 227, 233, 240, 244, 247) (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, 3, 5, 4)(6, 246)(7, 248, 10, 249)(8, 250, 9, 247)(11, 241)(12, 243, 15,
244)(13, 245, 14, 242)(16, 236)(17, 238, 20, 239)(18, 240, 19, 237)(21, 231)(22,
233, 25, 234)(23, 235, 24, 232)(26, 226)(27, 228, 30, 229)(28, 230, 29, 227)(31,
221)(32, 223, 35, 224)(33, 225, 34, 222)(36, 216)(37, 218, 40, 219)(38, 220, 39,
217)(41, 211)(42, 213, 45, 214)(43, 215, 44, 212)(46, 206)(47, 208, 50, 209)(48,
210, 49, 207)(51, 201)(52, 203, 55, 204)(53, 205, 54, 202)(56, 196)(57, 198, 60,
199)(58, 200, 59, 197)(61, 191)(62, 193, 65, 194)(63, 195, 64, 192)(66, 186)(67,
188, 70, 189)(68, 190, 69, 187)(71, 181)(72, 183, 75, 184)(73, 185, 74, 182)(76,
176)(77, 178, 80, 179)(78, 180, 79, 177)(81, 171)(82, 173, 85, 174)(83, 175, 84,
172)(86, 166)(87, 168, 90, 169)(88, 170, 89, 167)(91, 161)(92, 163, 95, 164)(93,
165, 94, 162)(96, 156)(97, 158, 100, 159)(98, 160, 99, 157)(101, 151)(102, 153,
105, 154)(103, 155, 104, 152)(106, 146)(107, 148, 110, 149)(108, 150, 109,
147)(111, 141)(112, 143, 115, 144)(113, 145, 114, 142)(116, 136)(117, 138, 120,
139)(118, 140, 119, 137)(121, 131)(122, 133, 125, 134)(123, 135, 124, 132)(127,
128, 130, 129)
c: (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)(212, 215)(213, 214)(217, 220)(218,
219)(222, 225)(223, 224)(227, 230)(228, 229)(232, 235)(233, 234)(237, 240)(238,
239)(242, 245)(243, 244)(247, 250)(248, 249)
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)(211, 212)(213, 215)(216, 217)(218,
220)(221, 222)(223, 225)(226, 227)(228, 230)(231, 232)(233, 235)(236, 237)(238,
240)(241, 242)(243, 245)(246, 247)(248, 250)
C4[ 250, 5 ]
250
-1 248 7 249 10
-2 6 249 8 250
-3 246 7 250 9
-4 246 247 8 10
-5 247 6 248 9
-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
-206 202 213 214 205
-207 201 203 214 215
-208 211 202 204 215
-209 211 212 203 205
-210 201 212 213 204
-211 209 220 217 208
-212 209 210 216 218
-213 210 206 217 219
-214 220 206 207 218
-215 216 207 208 219
-216 212 223 224 215
-217 211 213 224 225
-218 221 212 214 225
-219 221 222 213 215
-220 211 222 223 214
-221 227 218 219 230
-222 220 226 228 219
-223 220 216 227 229
-224 216 217 228 230
-225 226 217 218 229
-226 222 233 234 225
-227 221 223 234 235
-228 231 222 224 235
-229 231 232 223 225
-230 221 232 233 224
-231 237 228 229 240
-232 236 238 229 230
-233 226 237 239 230
-234 226 227 238 240
-235 236 227 228 239
-236 232 243 244 235
-237 231 233 244 245
-238 232 234 245 241
-239 242 233 235 241
-240 231 242 243 234
-241 247 238 239 250
-242 246 248 239 240
-243 236 247 249 240
-244 236 237 248 250
-245 246 237 238 249
-246 242 3 245 4
-247 243 4 5 241
-248 242 1 244 5
-249 1 243 2 245
-250 2 244 3 241
0