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