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On this page are computer-accessible forms for the graph C4[ 168, 63 ] = BGCG(MC3(6,14,1,10,3,0,1);K1;{1,3}).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {80, 92} under the group generated by the following permutations:

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

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

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