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On this page are computer-accessible forms for the graph C4[ 160, 69 ] = BGCG(KE_20(1,7,2,15,1);K1;{1,2}).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {70, 86} under the group generated by the following permutations:

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

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

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