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