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On this page are computer-accessible forms for the graph C4[ 160, 31 ] = PL(MC3(4,20,1,9,13,10,1),[8^10,10^8]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {75, 90} under the group generated by the following permutations:

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

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

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