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On this page are computer-accessible forms for the graph C4[ 160, 20 ] = MPS(4,80;7).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {80, 84} under the group generated by the following permutations:

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

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