Graph forms
for C4 [ 192, 212 ] = SS[192,112]
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On this page are computer-accessible forms for the graph C4[ 192, 212 ] =
SS[192,112].
(I) Following is a form readable by MAGMA:
g:=Graph<192|{ {1, 3}, {180, 182}, {152, 154}, {1, 2}, {1, 5}, {179, 183}, {152,
156}, {35, 39}, {34, 38}, {33, 37}, {1, 4}, {97, 103}, {177, 183}, {176, 182},
{152, 158}, {32, 39}, {151, 159}, {176, 185}, {178, 187}, {33, 43}, {178, 184},
{151, 157}, {36, 46}, {35, 41}, {33, 42}, {177, 186}, {36, 47}, {36, 40}, {151,
155}, {98, 110}, {34, 44}, {151, 153}, {99, 109}, {34, 45}, {180, 187}, {179,
188}, {96, 111}, {100, 116}, {138, 155}, {136, 154}, {174, 188}, {35, 48}, {172,
191}, {140, 159}, {171, 191}, {168, 190}, {175, 185}, {137, 158}, {175, 184},
{173, 186}, {139, 156}, {165, 189}, {173, 181}, {32, 57}, {167, 190}, {134,
157}, {174, 181}, {166, 189}, {164, 191}, {160, 187}, {32, 60}, {162, 190},
{161, 189}, {129, 157}, {130, 159}, {128, 158}, {135, 153}, {132, 155}, {9, 41},
{21, 53}, {16, 48}, {13, 45}, {12, 44}, {11, 43}, {69, 101}, {10, 43}, {157,
188}, {155, 186}, {28, 61}, {18, 51}, {17, 48}, {28, 62}, {14, 45}, {154, 185},
{131, 160}, {25, 58}, {22, 53}, {72, 107}, {94, 125}, {23, 51}, {156, 184},
{143, 171}, {91, 127}, {15, 42}, {133, 160}, {26, 63}, {20, 49}, {90, 127}, {16,
54}, {29, 59}, {19, 52}, {24, 63}, {80, 119}, {89, 126}, {85, 125}, {159, 183},
{158, 182}, {142, 166}, {141, 165}, {86, 126}, {17, 56}, {17, 59}, {64, 106},
{70, 108}, {88, 114}, {89, 115}, {16, 60}, {153, 181}, {67, 111}, {66, 110},
{65, 109}, {93, 113}, {24, 54}, {18, 61}, {95, 112}, {9, 57}, {14, 62}, {85,
101}, {75, 122}, {149, 164}, {76, 125}, {26, 40}, {71, 117}, {78, 124}, {91,
105}, {94, 108}, {11, 56}, {148, 167}, {68, 119}, {74, 121}, {68, 112}, {76,
120}, {79, 123}, {92, 104}, {71, 114}, {150, 163}, {74, 127}, {12, 58}, {67,
117}, {64, 118}, {24, 46}, {31, 40}, {150, 161}, {149, 162}, {73, 126}, {9, 49},
{152, 160}, {146, 170}, {145, 169}, {23, 47}, {77, 117}, {13, 52}, {14, 55},
{21, 47}, {29, 39}, {28, 38}, {30, 37}, {147, 168}, {86, 106}, {144, 172}, {87,
107}, {90, 102}, {10, 55}, {65, 124}, {19, 46}, {15, 50}, {69, 120}, {12, 50},
{66, 124}, {27, 37}, {20, 42}, {18, 44}, {70, 120}, {22, 41}, {25, 38}, {72,
119}, {73, 118}, {10, 72}, {59, 121}, {57, 123}, {8, 75}, {58, 121}, {24, 91},
{8, 76}, {8, 77}, {62, 123}, {17, 87}, {60, 122}, {8, 79}, {61, 122}, {60, 116},
{7, 78}, {63, 118}, {22, 95}, {15, 69}, {11, 71}, {63, 115}, {61, 113}, {13,
65}, {7, 74}, {29, 80}, {23, 90}, {7, 73}, {16, 94}, {19, 92}, {25, 73}, {31,
79}, {30, 78}, {27, 75}, {26, 74}, {28, 77}, {6, 84}, {59, 105}, {15, 93}, {23,
68}, {6, 82}, {22, 66}, {20, 64}, {13, 89}, {6, 83}, {19, 70}, {14, 88}, {62,
104}, {30, 72}, {21, 67}, {6, 81}, {7, 80}, {25, 65}, {31, 70}, {12, 86}, {9,
85}, {58, 102}, {31, 67}, {27, 71}, {26, 68}, {57, 103}, {30, 64}, {27, 69},
{29, 66}, {163, 192}, {10, 99}, {169, 192}, {170, 192}, {32, 76}, {11, 100},
{33, 81}, {34, 82}, {18, 96}, {21, 97}, {20, 98}, {35, 84}, {36, 83}, {45, 143},
{48, 147}, {43, 142}, {42, 141}, {37, 149}, {38, 150}, {39, 150}, {5, 183}, {55,
133}, {52, 135}, {49, 133}, {56, 140}, {50, 134}, {3, 182}, {50, 135}, {3, 181},
{2, 186}, {4, 188}, {53, 140}, {5, 191}, {51, 137}, {49, 139}, {2, 185}, {51,
136}, {44, 144}, {3, 190}, {54, 139}, {47, 146}, {41, 148}, {40, 149}, {5, 184},
{52, 138}, {56, 134}, {55, 137}, {54, 136}, {2, 189}, {53, 138}, {46, 145}, {4,
187}, {107, 171}, {103, 165}, {113, 179}, {114, 176}, {102, 165}, {112, 179},
{4, 192}, {109, 169}, {110, 170}, {106, 173}, {108, 171}, {89, 145}, {91, 147},
{111, 167}, {101, 172}, {102, 175}, {75, 129}, {90, 144}, {101, 175}, {103,
173}, {79, 132}, {77, 128}, {78, 131}, {93, 144}, {95, 146}, {106, 167}, {104,
166}, {94, 145}, {105, 166}, {80, 130}, {92, 143}, {119, 164}, {81, 133}, {118,
162}, {82, 135}, {87, 130}, {88, 142}, {81, 134}, {117, 162}, {84, 140}, {121,
161}, {85, 141}, {88, 128}, {92, 132}, {83, 138}, {122, 163}, {87, 142}, {104,
177}, {105, 176}, {107, 177}, {123, 161}, {110, 180}, {114, 168}, {116, 174},
{82, 137}, {83, 136}, {86, 141}, {111, 180}, {113, 170}, {115, 168}, {93, 129},
{112, 172}, {120, 164}, {95, 130}, {115, 174}, {116, 169}, {108, 178}, {84,
139}, {124, 163}, {109, 178}, {96, 128}, {99, 131}, {98, 131}, {125, 156}, {97,
132}, {127, 154}, {100, 129}, {126, 153}, {99, 143}, {96, 146}, {97, 148}, {98,
148}, {100, 147} }>;
(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, 6)(2, 81)(3, 82)(4, 83)(5, 84)(9, 101)(10, 105)(11, 104)(12, 106)(13,
115)(14, 114)(15, 103)(16, 108)(17, 107)(18, 111)(19, 116)(20, 102)(21, 113)(22,
112)(23, 110)(24, 109)(25, 118)(26, 124)(27, 123)(28, 117)(29, 119)(30, 121)(31,
122)(32, 120)(33, 189)(34, 190)(35, 191)(36, 192)(37, 161)(38, 162)(39, 164)(40,
163)(41, 172)(42, 165)(43, 166)(44, 167)(45, 168)(46, 169)(47, 170)(48, 171)(49,
175)(50, 173)(51, 180)(52, 174)(53, 179)(54, 178)(55, 176)(56, 177)(57, 69)(58,
64)(59, 72)(60, 70)(61, 67)(62, 71)(63, 65)(66, 68)(74, 78)(75, 79)(90, 98)(91,
99)(92, 100)(93, 97)(127, 131)(129, 132)(133, 185)(134, 186)(135, 181)(136,
187)(137, 182)(138, 188)(139, 184)(140, 183)(143, 147)(144, 148)(149, 150)(154,
160)(155, 157) (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: (2, 5, 4, 3)(7, 8)(9, 10, 18, 24)(11, 12, 19, 22)(13, 21, 17, 15)(14, 23, 16,
20)(25, 31, 29, 27)(26, 32, 30, 28)(33, 34, 36, 35)(37, 38, 40, 39)(41, 43, 44,
46)(42, 45, 47, 48)(49, 55, 51, 54)(50, 52, 53, 56)(57, 72, 61, 63)(58, 70, 66,
71)(59, 69, 65, 67)(60, 64, 62, 68)(73, 79, 80, 75)(74, 76, 78, 77)(81, 82, 83,
84)(85, 99, 96, 91)(86, 92, 95, 100)(87, 93, 89, 97)(88, 90, 94, 98)(101, 109,
111, 105)(102, 108, 110, 114)(103, 107, 113, 115)(104, 112, 116, 106)(117, 121,
120, 124)(118, 123, 119, 122)(125, 131, 128, 127)(126, 132, 130, 129)(133, 137,
136, 139)(134, 135, 138, 140)(141, 143, 146, 147)(142, 144, 145, 148)(149,
150)(153, 155, 159, 157)(154, 156, 160, 158)(161, 164, 163, 162)(165, 171, 170,
168)(166, 172, 169, 167)(173, 177, 179, 174)(175, 178, 180, 176)(181, 186, 183,
188)(182, 185, 184, 187)(189, 191, 192, 190)
c: (2, 4)(3, 5)(7, 8)(9, 13)(10, 21)(11, 23)(12, 16)(14, 22)(15, 24)(17, 18)(19,
20)(25, 32)(26, 27)(28, 29)(30, 31)(33, 36)(34, 35)(37, 40)(38, 39)(41, 45)(42,
46)(43, 47)(44, 48)(49, 52)(50, 54)(51, 56)(53, 55)(57, 65)(58, 60)(59, 61)(62,
66)(63, 69)(64, 70)(67, 72)(68, 71)(73, 76)(74, 75)(77, 80)(78, 79)(81, 83)(82,
84)(85, 89)(86, 94)(87, 96)(88, 95)(90, 100)(91, 93)(92, 98)(97, 99)(101,
115)(102, 116)(103, 109)(104, 110)(105, 113)(106, 108)(107, 111)(112, 114)(117,
119)(118, 120)(121, 122)(123, 124)(125, 126)(127, 129)(128, 130)(131, 132)(133,
138)(134, 136)(135, 139)(137, 140)(141, 145)(142, 146)(143, 148)(144, 147)(151,
152)(153, 156)(154, 157)(155, 160)(158, 159)(161, 163)(162, 164)(165, 169)(166,
170)(167, 171)(168, 172)(173, 178)(174, 175)(176, 179)(177, 180)(181, 184)(182,
183)(185, 188)(186, 187)(189, 192)(190, 191)
d: (1, 9)(2, 85)(3, 49)(4, 41)(5, 57)(6, 115)(7, 18)(8, 107)(10, 117)(12,
127)(13, 36)(14, 149)(15, 105)(16, 151)(17, 129)(20, 182)(21, 109)(22, 192)(23,
25)(24, 135)(26, 34)(27, 142)(28, 119)(29, 113)(30, 128)(31, 143)(32, 183)(33,
114)(35, 188)(37, 88)(38, 68)(39, 179)(40, 45)(42, 176)(43, 71)(44, 74)(46,
52)(47, 65)(48, 157)(50, 91)(51, 73)(53, 169)(54, 153)(55, 162)(56, 100)(58,
90)(59, 93)(60, 159)(61, 80)(62, 164)(63, 82)(64, 158)(66, 170)(67, 99)(69,
166)(70, 92)(72, 77)(75, 87)(76, 177)(78, 96)(79, 171)(81, 168)(83, 89)(84,
174)(86, 154)(94, 155)(95, 163)(97, 178)(98, 180)(101, 189)(103, 184)(104,
120)(106, 152)(108, 132)(111, 131)(112, 150)(116, 140)(118, 137)(121, 144)(122,
130)(123, 191)(124, 146)(125, 186)(126, 136)(133, 190)(134, 147)(138, 145)(139,
181)(141, 185)(148, 187)(156, 173)(160, 167)(161, 172)(165, 175)
e: (2, 3)(4, 5)(9, 11)(10, 22)(12, 24)(13, 23)(14, 21)(15, 16)(17, 20)(18,
19)(25, 26)(27, 32)(28, 31)(29, 30)(33, 35)(34, 36)(37, 39)(38, 40)(41, 43)(42,
48)(44, 46)(45, 47)(49, 56)(50, 54)(51, 52)(53, 55)(57, 71)(58, 63)(59, 64)(60,
69)(61, 70)(62, 67)(65, 68)(66, 72)(73, 74)(75, 76)(77, 79)(78, 80)(81, 84)(82,
83)(85, 100)(86, 91)(87, 98)(88, 97)(89, 90)(92, 96)(93, 94)(95, 99)(101,
116)(102, 115)(103, 114)(104, 111)(105, 106)(107, 110)(108, 113)(109, 112)(117,
123)(118, 121)(119, 124)(120, 122)(125, 129)(126, 127)(128, 132)(130, 131)(133,
140)(134, 139)(135, 136)(137, 138)(141, 147)(142, 148)(143, 146)(144, 145)(149,
150)(151, 152)(153, 154)(155, 158)(156, 157)(159, 160)(161, 162)(163, 164)(165,
168)(166, 167)(169, 172)(170, 171)(173, 176)(174, 175)(177, 180)(178, 179)(181,
185)(182, 186)(183, 187)(184, 188)(189, 190)(191, 192)
f: (1, 7)(2, 78)(3, 73)(4, 74)(5, 80)(6, 8)(10, 104)(11, 19)(12, 111)(13,
114)(15, 21)(17, 108)(20, 103)(22, 101)(23, 113)(24, 116)(25, 182)(26, 188)(27,
138)(28, 137)(29, 184)(30, 186)(31, 134)(32, 139)(33, 132)(34, 128)(35, 125)(36,
129)(37, 155)(38, 158)(39, 156)(40, 157)(41, 85)(42, 97)(43, 92)(44, 96)(45,
88)(46, 100)(47, 93)(48, 94)(49, 57)(50, 67)(51, 61)(52, 71)(53, 69)(54, 60)(55,
62)(56, 70)(58, 180)(59, 178)(63, 174)(64, 173)(65, 176)(66, 175)(68, 179)(72,
177)(75, 83)(76, 84)(77, 82)(79, 81)(86, 167)(87, 171)(89, 168)(90, 170)(91,
169)(95, 172)(98, 165)(99, 166)(102, 110)(105, 109)(117, 135)(118, 181)(119,
183)(120, 140)(121, 187)(122, 136)(123, 133)(124, 185)(126, 190)(127, 192)(130,
191)(131, 189)(141, 148)(142, 143)(144, 146)(145, 147)(149, 151)(150, 152)(153,
162)(154, 163)(159, 164)(160, 161)
C4[ 192, 212 ]
192
-1 2 3 4 5
-2 1 189 185 186
-3 1 190 181 182
-4 187 1 188 192
-5 1 191 183 184
-6 81 82 83 84
-7 78 80 73 74
-8 77 79 75 76
-9 57 49 41 85
-10 55 99 72 43
-11 56 100 71 43
-12 44 58 50 86
-13 45 89 52 65
-14 55 88 45 62
-15 69 93 50 42
-16 48 60 94 54
-17 56 48 59 87
-18 44 61 51 96
-19 46 70 92 52
-20 49 42 64 98
-21 67 47 53 97
-22 66 95 41 53
-23 68 90 47 51
-24 46 91 63 54
-25 58 38 73 65
-26 68 40 63 74
-27 69 37 71 75
-28 77 38 61 62
-29 66 80 59 39
-30 78 37 72 64
-31 67 79 70 40
-32 57 60 39 76
-33 37 81 42 43
-34 44 45 38 82
-35 48 39 84 41
-36 46 47 83 40
-37 33 27 149 30
-38 34 25 28 150
-39 35 29 150 32
-40 36 26 149 31
-41 22 35 148 9
-42 33 15 20 141
-43 11 33 10 142
-44 12 34 144 18
-45 143 34 13 14
-46 24 145 36 19
-47 23 36 146 21
-48 35 147 16 17
-49 133 139 9 20
-50 12 134 135 15
-51 23 136 137 18
-52 13 135 138 19
-53 22 138 140 21
-54 24 136 16 139
-55 133 14 137 10
-56 11 134 17 140
-57 123 103 9 32
-58 121 12 25 102
-59 121 17 105 29
-60 122 16 116 32
-61 122 113 28 18
-62 123 14 104 28
-63 24 26 115 118
-64 106 30 118 20
-65 13 25 124 109
-66 22 110 124 29
-67 111 117 31 21
-68 23 112 26 119
-69 101 15 27 120
-70 19 31 108 120
-71 11 114 27 117
-72 30 107 119 10
-73 25 126 7 118
-74 121 26 127 7
-75 122 27 8 129
-76 125 8 32 120
-77 28 117 128 8
-78 124 7 30 131
-79 132 123 8 31
-80 7 29 119 130
-81 33 133 134 6
-82 34 135 137 6
-83 36 136 6 138
-84 35 6 139 140
-85 101 125 9 141
-86 12 126 106 141
-87 17 107 130 142
-88 14 114 128 142
-89 13 145 115 126
-90 23 144 102 127
-91 24 147 105 127
-92 132 143 104 19
-93 144 113 15 129
-94 145 125 16 108
-95 22 112 146 130
-96 111 146 18 128
-97 132 103 148 21
-98 110 148 20 131
-99 143 10 109 131
-100 11 147 116 129
-101 69 172 85 175
-102 165 90 58 175
-103 165 57 173 97
-104 166 177 92 62
-105 176 166 91 59
-106 167 173 64 86
-107 177 72 171 87
-108 178 70 94 171
-109 99 178 169 65
-110 66 180 170 98
-111 67 167 180 96
-112 68 179 95 172
-113 179 93 170 61
-114 88 176 168 71
-115 89 168 63 174
-116 100 169 60 174
-117 77 67 71 162
-118 73 63 162 64
-119 68 80 72 164
-120 69 70 76 164
-121 58 59 161 74
-122 60 61 75 163
-123 57 79 62 161
-124 66 78 163 65
-125 156 94 85 76
-126 89 73 86 153
-127 154 90 91 74
-128 77 88 158 96
-129 100 157 93 75
-130 80 159 95 87
-131 99 78 160 98
-132 155 79 92 97
-133 55 81 49 160
-134 56 157 81 50
-135 82 50 52 153
-136 154 83 51 54
-137 55 158 82 51
-138 155 83 52 53
-139 156 49 84 54
-140 56 159 84 53
-141 165 85 42 86
-142 88 166 43 87
-143 99 45 92 171
-144 44 90 93 172
-145 89 46 169 94
-146 47 170 95 96
-147 100 91 168 48
-148 167 41 97 98
-149 37 40 162 164
-150 38 39 161 163
-151 155 157 159 153
-152 154 156 158 160
-153 135 126 181 151
-154 136 127 152 185
-155 132 138 151 186
-156 125 139 184 152
-157 188 134 129 151
-158 137 182 128 152
-159 183 140 151 130
-160 187 133 152 131
-161 121 123 189 150
-162 190 149 117 118
-163 122 124 192 150
-164 191 149 119 120
-165 189 102 103 141
-166 189 104 105 142
-167 111 190 148 106
-168 190 114 147 115
-169 145 192 116 109
-170 110 113 146 192
-171 143 191 107 108
-172 144 101 112 191
-173 103 181 106 186
-174 188 115 181 116
-175 101 102 184 185
-176 114 105 182 185
-177 104 183 107 186
-178 187 184 108 109
-179 188 112 113 183
-180 110 187 111 182
-181 3 173 174 153
-182 176 3 158 180
-183 177 179 5 159
-184 156 178 5 175
-185 154 176 2 175
-186 155 177 2 173
-187 178 4 180 160
-188 157 179 4 174
-189 165 166 2 161
-190 167 3 168 162
-191 5 171 172 164
-192 4 169 170 163
0