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On this page are computer-accessible forms for the graph C4[ 160, 16 ] = MPS(8,40;3).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {40, 42} under the group generated by the following permutations:

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

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

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