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On this page are computer-accessible forms for the graph C4[ 160, 75 ] = BGCG(UG(Cmap(160,9){8,4|5}_10);K1;5).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {72, 88} under the group generated by the following permutations:

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

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

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