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