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