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On this page are computer-accessible forms for the graph C4[ 168, 37 ] = UG(ATD[168,19]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {12, 13} under the group generated by the following permutations:

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

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

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