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On this page are computer-accessible forms for the graph C4[ 160, 74 ] = BGCG(UG(Cmap(160,9){8,4|5}_10);K1;4).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {80, 81} under the group generated by the following permutations:

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

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

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