C4graphGraph forms for C4 [ 192, 85 ] = UG(ATD[192,35])

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On this page are computer-accessible forms for the graph C4[ 192, 85 ] = UG(ATD[192,35]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {44, 45} under the group generated by the following permutations:

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

(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.

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

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