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On this page are computer-accessible forms for the graph C4[ 168, 64 ] = BGCG(UG(ATD[84,23]);K1;{4,6}).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {82, 86} under the group generated by the following permutations:

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

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

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