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On this page are computer-accessible forms for the graph C4[ 168, 36 ] = UG(ATD[168,17]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {20, 22} under the group generated by the following permutations:

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

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

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