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