Graph forms
for C4 [ 224, 12 ] = PX(28,3)
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On this page are computer-accessible forms for the graph C4[ 224, 12 ] =
PX(28,3).
(I) Following is a form readable by MAGMA:
g:=Graph<224|{ {8, 15}, {216, 223}, {208, 215}, {200, 207}, {192, 199}, {184,
191}, {176, 183}, {96, 103}, {88, 95}, {80, 87}, {72, 79}, {16, 23}, {24, 31},
{32, 39}, {40, 47}, {48, 55}, {56, 63}, {64, 71}, {104, 111}, {112, 119}, {120,
127}, {128, 135}, {136, 143}, {144, 151}, {152, 159}, {160, 167}, {168, 175},
{1, 9}, {209, 217}, {208, 216}, {193, 201}, {192, 200}, {177, 185}, {176, 184},
{97, 105}, {96, 104}, {81, 89}, {80, 88}, {16, 24}, {17, 25}, {32, 40}, {33,
41}, {48, 56}, {49, 57}, {64, 72}, {65, 73}, {112, 120}, {113, 121}, {128, 136},
{129, 137}, {144, 152}, {145, 153}, {160, 168}, {161, 169}, {2, 11}, {215, 222},
{210, 219}, {199, 206}, {194, 203}, {183, 190}, {178, 187}, {103, 110}, {98,
107}, {87, 94}, {82, 91}, {71, 78}, {66, 75}, {7, 14}, {18, 27}, {23, 30}, {34,
43}, {39, 46}, {50, 59}, {55, 62}, {114, 123}, {119, 126}, {130, 139}, {135,
142}, {146, 155}, {151, 158}, {162, 171}, {167, 174}, {6, 12}, {215, 221}, {214,
220}, {199, 205}, {198, 204}, {183, 189}, {182, 188}, {103, 109}, {102, 108},
{87, 93}, {86, 92}, {71, 77}, {70, 76}, {7, 13}, {22, 28}, {23, 29}, {38, 44},
{39, 45}, {54, 60}, {55, 61}, {118, 124}, {119, 125}, {134, 140}, {135, 141},
{150, 156}, {151, 157}, {166, 172}, {167, 173}, {1, 10}, {212, 223}, {209, 218},
{196, 207}, {193, 202}, {180, 191}, {177, 186}, {100, 111}, {97, 106}, {84, 95},
{81, 90}, {68, 79}, {65, 74}, {4, 15}, {17, 26}, {20, 31}, {33, 42}, {36, 47},
{49, 58}, {52, 63}, {113, 122}, {116, 127}, {129, 138}, {132, 143}, {145, 154},
{148, 159}, {161, 170}, {164, 175}, {5, 9}, {213, 217}, {197, 201}, {181, 185},
{101, 105}, {85, 89}, {69, 73}, {21, 25}, {37, 41}, {53, 57}, {117, 121}, {133,
137}, {149, 153}, {165, 169}, {3, 14}, {214, 219}, {211, 222}, {198, 203}, {195,
206}, {182, 187}, {179, 190}, {102, 107}, {99, 110}, {86, 91}, {83, 94}, {70,
75}, {67, 78}, {6, 11}, {19, 30}, {22, 27}, {35, 46}, {38, 43}, {51, 62}, {54,
59}, {115, 126}, {118, 123}, {131, 142}, {134, 139}, {147, 158}, {150, 155},
{163, 174}, {166, 171}, {2, 12}, {211, 221}, {210, 220}, {195, 205}, {194, 204},
{179, 189}, {178, 188}, {99, 109}, {98, 108}, {83, 93}, {82, 92}, {67, 77}, {66,
76}, {3, 13}, {18, 28}, {19, 29}, {34, 44}, {35, 45}, {50, 60}, {51, 61}, {114,
124}, {115, 125}, {130, 140}, {131, 141}, {146, 156}, {147, 157}, {162, 172},
{163, 173}, {5, 10}, {213, 218}, {197, 202}, {181, 186}, {101, 106}, {85, 90},
{69, 74}, {21, 26}, {37, 42}, {53, 58}, {117, 122}, {133, 138}, {149, 154},
{165, 170}, {4, 16}, {204, 216}, {196, 208}, {100, 112}, {76, 88}, {68, 80},
{12, 24}, {36, 48}, {44, 56}, {108, 120}, {132, 144}, {140, 152}, {164, 176},
{172, 184}, {8, 16}, {201, 209}, {200, 208}, {73, 81}, {72, 80}, {9, 17}, {40,
48}, {41, 49}, {104, 112}, {105, 113}, {136, 144}, {137, 145}, {168, 176}, {169,
177}, {10, 19}, {207, 214}, {202, 211}, {175, 182}, {79, 86}, {74, 83}, {15,
22}, {42, 51}, {47, 54}, {106, 115}, {111, 118}, {138, 147}, {143, 150}, {170,
179}, {14, 20}, {207, 213}, {206, 212}, {175, 181}, {79, 85}, {78, 84}, {15,
21}, {46, 52}, {47, 53}, {110, 116}, {111, 117}, {142, 148}, {143, 149}, {174,
180}, {9, 18}, {204, 215}, {201, 210}, {76, 87}, {73, 82}, {12, 23}, {41, 50},
{44, 55}, {105, 114}, {108, 119}, {137, 146}, {140, 151}, {169, 178}, {172,
183}, {13, 17}, {205, 209}, {77, 81}, {45, 49}, {109, 113}, {141, 145}, {173,
177}, {11, 22}, {206, 211}, {203, 214}, {78, 83}, {75, 86}, {14, 19}, {43, 54},
{46, 51}, {107, 118}, {110, 115}, {139, 150}, {142, 147}, {171, 182}, {174,
179}, {10, 20}, {203, 213}, {202, 212}, {75, 85}, {74, 84}, {11, 21}, {42, 52},
{43, 53}, {106, 116}, {107, 117}, {138, 148}, {139, 149}, {170, 180}, {171,
181}, {13, 18}, {205, 210}, {77, 82}, {45, 50}, {109, 114}, {141, 146}, {173,
178}, {20, 32}, {212, 224}, {92, 104}, {84, 96}, {28, 40}, {148, 160}, {156,
168}, {24, 32}, {216, 224}, {89, 97}, {88, 96}, {25, 33}, {152, 160}, {153,
161}, {26, 35}, {95, 102}, {90, 99}, {31, 38}, {154, 163}, {159, 166}, {30, 36},
{95, 101}, {94, 100}, {31, 37}, {158, 164}, {159, 165}, {25, 34}, {92, 103},
{89, 98}, {28, 39}, {153, 162}, {156, 167}, {29, 33}, {93, 97}, {157, 161}, {27,
38}, {94, 99}, {91, 102}, {30, 35}, {155, 166}, {158, 163}, {26, 36}, {91, 101},
{90, 100}, {27, 37}, {154, 164}, {155, 165}, {29, 34}, {93, 98}, {157, 162},
{52, 64}, {188, 200}, {180, 192}, {60, 72}, {56, 64}, {185, 193}, {184, 192},
{57, 65}, {58, 67}, {191, 198}, {186, 195}, {63, 70}, {62, 68}, {191, 197},
{190, 196}, {63, 69}, {57, 66}, {188, 199}, {185, 194}, {60, 71}, {61, 65},
{189, 193}, {59, 70}, {190, 195}, {187, 198}, {62, 67}, {58, 68}, {187, 197},
{186, 196}, {59, 69}, {61, 66}, {189, 194}, {8, 220}, {1, 217}, {3, 218}, {6,
223}, {4, 222}, {5, 223}, {2, 217}, {7, 220}, {1, 221}, {3, 222}, {6, 219}, {4,
218}, {5, 219}, {2, 221}, {7, 224}, {8, 224}, {116, 128}, {124, 136}, {120,
128}, {121, 129}, {122, 131}, {127, 134}, {126, 132}, {127, 133}, {121, 130},
{124, 135}, {125, 129}, {123, 134}, {126, 131}, {122, 132}, {123, 133}, {125,
130} }>;
(II) A more general form is to represent the graph as the orbit of {8, 15}
under the group generated by the following permutations:
a: (2, 5)(4, 7)(9, 217)(10, 221)(11, 219)(12, 223)(13, 218)(14, 222)(15,
220)(16, 224)(17, 209)(18, 213)(19, 211)(20, 215)(21, 210)(22, 214)(23, 212)(24,
216)(25, 201)(26, 205)(27, 203)(28, 207)(29, 202)(30, 206)(31, 204)(32, 208)(33,
193)(34, 197)(35, 195)(36, 199)(37, 194)(38, 198)(39, 196)(40, 200)(41, 185)(42,
189)(43, 187)(44, 191)(45, 186)(46, 190)(47, 188)(48, 192)(49, 177)(50, 181)(51,
179)(52, 183)(53, 178)(54, 182)(55, 180)(56, 184)(57, 169)(58, 173)(59, 171)(60,
175)(61, 170)(62, 174)(63, 172)(64, 176)(65, 161)(66, 165)(67, 163)(68, 167)(69,
162)(70, 166)(71, 164)(72, 168)(73, 153)(74, 157)(75, 155)(76, 159)(77, 154)(78,
158)(79, 156)(80, 160)(81, 145)(82, 149)(83, 147)(84, 151)(85, 146)(86, 150)(87,
148)(88, 152)(89, 137)(90, 141)(91, 139)(92, 143)(93, 138)(94, 142)(95, 140)(96,
144)(97, 129)(98, 133)(99, 131)(100, 135)(101, 130)(102, 134)(103, 132)(104,
136)(105, 121)(106, 125)(107, 123)(108, 127)(109, 122)(110, 126)(111, 124)(112,
128)(114, 117)(116, 119) (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: (177, 178)(179, 180)(181, 182)(183, 184)(185, 187)(186, 188)(189, 191)(190,
192)(193, 197)(194, 198)(195, 199)(196, 200)
c: (81, 82)(83, 84)(85, 86)(87, 88)(89, 91)(90, 92)(93, 95)(94, 96)(97, 101)(98,
102)(99, 103)(100, 104)
d: (145, 146)(147, 148)(149, 150)(151, 152)(153, 155)(154, 156)(157, 159)(158,
160)(161, 165)(162, 166)(163, 167)(164, 168)
e: (113, 114)(115, 116)(117, 118)(119, 120)(121, 123)(122, 124)(125, 127)(126,
128)(129, 133)(130, 134)(131, 135)(132, 136)
f: (49, 50)(51, 52)(53, 54)(55, 56)(57, 59)(58, 60)(61, 63)(62, 64)(65, 69)(66,
70)(67, 71)(68, 72)
g: (17, 18)(19, 20)(21, 22)(23, 24)(25, 27)(26, 28)(29, 31)(30, 32)(33, 37)(34,
38)(35, 39)(36, 40)
h: (201, 202)(203, 204)(205, 206)(207, 208)(209, 211)(210, 212)(213, 215)(214,
216)(217, 221)(218, 222)(219, 223)(220, 224)
m: (73, 74)(75, 76)(77, 78)(79, 80)(81, 83)(82, 84)(85, 87)(86, 88)(89, 93)(90,
94)(91, 95)(92, 96)
n1: (105, 106)(107, 108)(109, 110)(111, 112)(113, 115)(114, 116)(117, 119)(118,
120)(121, 125)(122, 126)(123, 127)(124, 128)
a1: (137, 138)(139, 140)(141, 142)(143, 144)(145, 147)(146, 148)(149, 151)(150,
152)(153, 157)(154, 158)(155, 159)(156, 160)
b1: (169, 170)(171, 172)(173, 174)(175, 176)(177, 179)(178, 180)(181, 183)(182,
184)(185, 189)(186, 190)(187, 191)(188, 192)
c1: (41, 42)(43, 44)(45, 46)(47, 48)(49, 51)(50, 52)(53, 55)(54, 56)(57, 61)(58,
62)(59, 63)(60, 64)
d1: (9, 10)(11, 12)(13, 14)(15, 16)(17, 19)(18, 20)(21, 23)(22, 24)(25, 29)(26,
30)(27, 31)(28, 32)
e1: (193, 194)(195, 196)(197, 198)(199, 200)(201, 203)(202, 204)(205, 207)(206,
208)(209, 213)(210, 214)(211, 215)(212, 216)
f1: (97, 98)(99, 100)(101, 102)(103, 104)(105, 107)(106, 108)(109, 111)(110,
112)(113, 117)(114, 118)(115, 119)(116, 120)
g1: (161, 162)(163, 164)(165, 166)(167, 168)(169, 171)(170, 172)(173, 175)(174,
176)(177, 181)(178, 182)(179, 183)(180, 184)
h1: (129, 130)(131, 132)(133, 134)(135, 136)(137, 139)(138, 140)(141, 143)(142,
144)(145, 149)(146, 150)(147, 151)(148, 152)
m1: (65, 66)(67, 68)(69, 70)(71, 72)(73, 75)(74, 76)(77, 79)(78, 80)(81, 85)(82,
86)(83, 87)(84, 88)
n2: (33, 34)(35, 36)(37, 38)(39, 40)(41, 43)(42, 44)(45, 47)(46, 48)(49, 53)(50,
54)(51, 55)(52, 56)
a2: (1, 2)(3, 4)(5, 6)(7, 8)(9, 11)(10, 12)(13, 15)(14, 16)(17, 21)(18, 22)(19,
23)(20, 24)
b2: (185, 186)(187, 188)(189, 190)(191, 192)(193, 195)(194, 196)(197, 199)(198,
200)(201, 205)(202, 206)(203, 207)(204, 208)
c2: (89, 90)(91, 92)(93, 94)(95, 96)(97, 99)(98, 100)(101, 103)(102, 104)(105,
109)(106, 110)(107, 111)(108, 112)
d2: (153, 154)(155, 156)(157, 158)(159, 160)(161, 163)(162, 164)(165, 167)(166,
168)(169, 173)(170, 174)(171, 175)(172, 176)
e2: (121, 122)(123, 124)(125, 126)(127, 128)(129, 131)(130, 132)(133, 135)(134,
136)(137, 141)(138, 142)(139, 143)(140, 144)
f2: (57, 58)(59, 60)(61, 62)(63, 64)(65, 67)(66, 68)(69, 71)(70, 72)(73, 77)(74,
78)(75, 79)(76, 80)
g2: (25, 26)(27, 28)(29, 30)(31, 32)(33, 35)(34, 36)(37, 39)(38, 40)(41, 45)(42,
46)(43, 47)(44, 48)
h2: (1, 3)(2, 4)(5, 7)(6, 8)(9, 13)(10, 14)(11, 15)(12, 16)(217, 218)(219,
220)(221, 222)(223, 224)
m2: (1, 9, 17, 25, 33, 41, 49, 57, 65, 73, 81, 89, 97, 105, 113, 121, 129, 137,
145, 153, 161, 169, 177, 185, 193, 201, 209, 217)(2, 10, 18, 26, 34, 42, 50, 58,
66, 74, 82, 90, 98, 106, 114, 122, 130, 138, 146, 154, 162, 170, 178, 186, 194,
202, 210, 218)(3, 11, 19, 27, 35, 43, 51, 59, 67, 75, 83, 91, 99, 107, 115, 123,
131, 139, 147, 155, 163, 171, 179, 187, 195, 203, 211, 219)(4, 12, 20, 28, 36,
44, 52, 60, 68, 76, 84, 92, 100, 108, 116, 124, 132, 140, 148, 156, 164, 172,
180, 188, 196, 204, 212, 220)(5, 13, 21, 29, 37, 45, 53, 61, 69, 77, 85, 93,
101, 109, 117, 125, 133, 141, 149, 157, 165, 173, 181, 189, 197, 205, 213,
221)(6, 14, 22, 30, 38, 46, 54, 62, 70, 78, 86, 94, 102, 110, 118, 126, 134,
142, 150, 158, 166, 174, 182, 190, 198, 206, 214, 222)(7, 15, 23, 31, 39, 47,
55, 63, 71, 79, 87, 95, 103, 111, 119, 127, 135, 143, 151, 159, 167, 175, 183,
191, 199, 207, 215, 223)(8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104,
112, 120, 128, 136, 144, 152, 160, 168, 176, 184, 192, 200, 208, 216, 224)
C4[ 224, 12 ]
224
-1 221 217 9 10
-2 11 12 221 217
-3 13 222 14 218
-4 222 15 16 218
-5 223 9 10 219
-6 11 12 223 219
-7 220 13 14 224
-8 220 15 224 16
-9 1 5 17 18
-10 1 5 19 20
-11 22 2 6 21
-12 23 2 24 6
-13 3 17 7 18
-14 3 7 19 20
-15 22 4 8 21
-16 23 24 4 8
-17 13 25 26 9
-18 13 27 28 9
-19 14 29 30 10
-20 14 31 10 32
-21 11 25 15 26
-22 11 15 27 28
-23 12 16 29 30
-24 12 16 31 32
-25 33 34 17 21
-26 35 36 17 21
-27 22 37 38 18
-28 22 39 18 40
-29 33 23 34 19
-30 23 35 36 19
-31 24 37 38 20
-32 24 39 40 20
-33 25 29 41 42
-34 44 25 29 43
-35 45 46 26 30
-36 47 26 48 30
-37 27 41 31 42
-38 44 27 31 43
-39 45 46 28 32
-40 47 48 28 32
-41 33 37 49 50
-42 33 37 51 52
-43 34 38 53 54
-44 55 34 56 38
-45 35 49 39 50
-46 35 39 51 52
-47 36 40 53 54
-48 55 56 36 40
-49 45 57 58 41
-50 45 59 60 41
-51 46 61 62 42
-52 46 63 42 64
-53 57 47 58 43
-54 47 59 60 43
-55 44 48 61 62
-56 44 48 63 64
-57 66 49 53 65
-58 67 68 49 53
-59 69 70 50 54
-60 71 50 72 54
-61 55 66 51 65
-62 55 67 68 51
-63 56 69 70 52
-64 56 71 72 52
-65 57 61 73 74
-66 57 61 75 76
-67 77 78 58 62
-68 79 58 80 62
-69 59 73 63 74
-70 59 63 75 76
-71 77 78 60 64
-72 79 80 60 64
-73 69 81 82 65
-74 69 83 84 65
-75 66 70 85 86
-76 66 88 70 87
-77 67 81 71 82
-78 67 71 83 84
-79 68 72 85 86
-80 88 68 72 87
-81 77 89 90 73
-82 77 91 92 73
-83 78 93 94 74
-84 78 95 74 96
-85 89 79 90 75
-86 79 91 92 75
-87 80 93 94 76
-88 80 95 96 76
-89 81 85 97 98
-90 99 100 81 85
-91 101 102 82 86
-92 103 82 104 86
-93 83 97 87 98
-94 99 100 83 87
-95 88 101 102 84
-96 88 103 104 84
-97 89 93 105 106
-98 89 93 107 108
-99 110 90 94 109
-100 111 90 112 94
-101 91 105 95 106
-102 91 95 107 108
-103 110 92 96 109
-104 111 112 92 96
-105 101 113 114 97
-106 101 115 116 97
-107 102 117 118 98
-108 102 119 98 120
-109 99 113 103 114
-110 99 103 115 116
-111 100 104 117 118
-112 100 104 119 120
-113 121 122 105 109
-114 123 124 105 109
-115 110 125 126 106
-116 110 127 106 128
-117 121 111 122 107
-118 111 123 124 107
-119 112 125 126 108
-120 112 127 128 108
-121 113 117 129 130
-122 132 113 117 131
-123 133 134 114 118
-124 135 114 136 118
-125 115 129 119 130
-126 132 115 119 131
-127 133 134 116 120
-128 135 136 116 120
-129 121 125 137 138
-130 121 125 139 140
-131 122 126 141 142
-132 143 122 144 126
-133 123 137 127 138
-134 123 127 139 140
-135 124 128 141 142
-136 143 144 124 128
-137 133 145 146 129
-138 133 147 148 129
-139 134 149 150 130
-140 134 151 130 152
-141 145 135 146 131
-142 135 147 148 131
-143 132 136 149 150
-144 132 136 151 152
-145 154 137 141 153
-146 155 156 137 141
-147 157 158 138 142
-148 159 138 160 142
-149 143 154 139 153
-150 143 155 156 139
-151 144 157 158 140
-152 144 159 160 140
-153 145 149 161 162
-154 145 149 163 164
-155 165 166 146 150
-156 167 146 168 150
-157 147 161 151 162
-158 147 151 163 164
-159 165 166 148 152
-160 167 168 148 152
-161 157 169 170 153
-162 157 171 172 153
-163 154 158 173 174
-164 154 176 158 175
-165 155 169 159 170
-166 155 159 171 172
-167 156 160 173 174
-168 176 156 160 175
-169 165 177 178 161
-170 165 179 180 161
-171 166 181 182 162
-172 166 183 162 184
-173 177 167 178 163
-174 167 179 180 163
-175 168 181 182 164
-176 168 183 184 164
-177 169 173 185 186
-178 187 188 169 173
-179 189 190 170 174
-180 191 170 192 174
-181 171 185 175 186
-182 187 188 171 175
-183 176 189 190 172
-184 176 191 192 172
-185 177 181 193 194
-186 177 181 195 196
-187 198 178 182 197
-188 199 178 200 182
-189 179 193 183 194
-190 179 183 195 196
-191 198 180 184 197
-192 199 200 180 184
-193 189 201 202 185
-194 189 203 204 185
-195 190 205 206 186
-196 190 207 186 208
-197 187 201 191 202
-198 187 191 203 204
-199 188 192 205 206
-200 188 192 207 208
-201 209 210 193 197
-202 211 212 193 197
-203 198 213 214 194
-204 198 215 194 216
-205 209 199 210 195
-206 199 211 212 195
-207 200 213 214 196
-208 200 215 216 196
-209 201 205 217 218
-210 220 201 205 219
-211 221 222 202 206
-212 223 202 224 206
-213 203 217 207 218
-214 220 203 207 219
-215 221 222 204 208
-216 223 224 204 208
-217 209 1 2 213
-218 209 3 4 213
-219 210 5 214 6
-220 210 214 7 8
-221 1 2 211 215
-222 211 3 4 215
-223 212 5 6 216
-224 212 7 216 8
0