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On this page are computer-accessible forms for the graph C4[ 160, 13 ] = MPS(16,20;3).

(I) Following is a form readable by MAGMA:

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

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

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

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