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