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On this page are computer-accessible forms for the graph C4[ 160, 21 ] = MPS(4,80;19).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {80, 90} under the group generated by the following permutations:

a: (3, 93)(23, 113)(42, 152)(62, 132)
b: (1, 2)(3, 20)(4, 19)(5, 18)(6, 17)(7, 16)(8, 15)(9, 14)(10, 13)(11, 12)(21, 22)(23, 40)(24, 39)(25, 38)(26, 37)(27, 36)(28, 35)(29, 34)(30, 33)(31, 32)(42, 130)(43, 59)(44, 58)(45, 57)(46, 56)(47, 55)(48, 54)(49, 53)(50, 52)(60, 132)(62, 150)(63, 79)(64, 78)(65, 77)(66, 76)(67, 75)(68, 74)(69, 73)(70, 72)(80, 152)(81, 102)(82, 101)(83, 100)(84, 99)(85, 98)(86, 97)(87, 96)(88, 95)(89, 94)(90, 93)(91, 112)(92, 111)(103, 120)(104, 119)(105, 118)(106, 117)(107, 116)(108, 115)(109, 114)(110, 113)(121, 141)(122, 140)(123, 139)(124, 138)(125, 137)(126, 136)(127, 135)(128, 134)(129, 133)(131, 151)(142, 160)(143, 159)(144, 158)(145, 157)(146, 156)(147, 155)(148, 154)(149, 153)
c: (7, 27)(46, 156)(47, 137)(66, 136)(67, 157)(97, 117)
d: (13, 83)(33, 103)(53, 143)(73, 123)
e: (4, 24)(43, 153)(44, 134)(63, 133)(64, 154)(94, 114)
f: (14, 34)(53, 123)(54, 144)(73, 143)(74, 124)(84, 104)
g: (20, 90)(40, 110)(60, 150)(80, 130)
h: (4, 94)(24, 114)(43, 153)(63, 133)
m: (13, 33)(52, 122)(53, 143)(72, 142)(73, 123)(83, 103)
n1: (16, 86)(36, 106)(56, 146)(76, 126)
a1: (19, 89)(39, 109)(59, 149)(79, 129)
b1: (18, 88)(38, 108)(58, 148)(78, 128)
c1: (16, 36)(55, 125)(56, 146)(75, 145)(76, 126)(86, 106)
d1: (19, 39)(58, 128)(59, 149)(78, 148)(79, 129)(89, 109)
e1: (5, 25)(44, 154)(45, 135)(64, 134)(65, 155)(95, 115)
f1: (7, 97)(27, 117)(46, 156)(66, 136)
g1: (15, 35)(54, 124)(55, 145)(74, 144)(75, 125)(85, 105)
h1: (3, 23)(42, 152)(43, 133)(62, 132)(63, 153)(93, 113)
m1: (12, 82)(32, 102)(52, 142)(72, 122)
n2: (17, 37)(56, 126)(57, 147)(76, 146)(77, 127)(87, 107)
a2: (6, 96)(26, 116)(45, 155)(65, 135)
b2: (18, 38)(57, 127)(58, 148)(77, 147)(78, 128)(88, 108)
c2: (17, 87)(37, 107)(57, 147)(77, 127)
d2: (5, 95)(25, 115)(44, 154)(64, 134)
e2: (6, 26)(45, 155)(46, 136)(65, 135)(66, 156)(96, 116)
f2: (10, 100)(30, 120)(49, 159)(69, 139)
g2: (15, 85)(35, 105)(55, 145)(75, 125)
h2: (2, 20)(3, 19)(4, 18)(5, 17)(6, 16)(7, 15)(8, 14)(9, 13)(10, 12)(22, 40)(23, 39)(24, 38)(25, 37)(26, 36)(27, 35)(28, 34)(29, 33)(30, 32)(41, 130)(42, 59)(43, 58)(44, 57)(45, 56)(46, 55)(47, 54)(48, 53)(49, 52)(50, 51)(60, 131)(61, 150)(62, 79)(63, 78)(64, 77)(65, 76)(66, 75)(67, 74)(68, 73)(69, 72)(70, 71)(80, 151)(81, 101)(82, 100)(83, 99)(84, 98)(85, 97)(86, 96)(87, 95)(88, 94)(89, 93)(90, 92)(91, 111)(102, 120)(103, 119)(104, 118)(105, 117)(106, 116)(107, 115)(108, 114)(109, 113)(110, 112)(121, 140)(122, 139)(123, 138)(124, 137)(125, 136)(126, 135)(127, 134)(128, 133)(129, 132)(141, 160)(142, 159)(143, 158)(144, 157)(145, 156)(146, 155)(147, 154)(148, 153)(149, 152)
m2: (9, 99)(29, 119)(48, 158)(68, 138)
n3: (8, 28)(47, 157)(48, 138)(67, 137)(68, 158)(98, 118)
a3: (11, 81)(31, 101)(51, 141)(71, 121)
b3: (14, 84)(34, 104)(54, 144)(74, 124)
c3: (1, 41, 2, 42, 3, 43, 4, 44, 5, 45, 6, 46, 7, 47, 8, 48, 9, 49, 10, 50, 11, 51, 12, 52, 13, 53, 14, 54, 15, 55, 16, 56, 17, 57, 18, 58, 19, 59, 20, 60, 21, 61, 22, 62, 23, 63, 24, 64, 25, 65, 26, 66, 27, 67, 28, 68, 29, 69, 30, 70, 31, 71, 32, 72, 33, 73, 34, 74, 35, 75, 36, 76, 37, 77, 38, 78, 39, 79, 40, 80)(81, 121, 82, 122, 83, 123, 84, 124, 85, 125, 86, 126, 87, 127, 88, 128, 89, 129, 90, 130, 91, 131, 92, 132, 93, 133, 94, 134, 95, 135, 96, 136, 97, 137, 98, 138, 99, 139, 100, 140, 101, 141, 102, 142, 103, 143, 104, 144, 105, 145, 106, 146, 107, 147, 108, 148, 109, 149, 110, 150, 111, 151, 112, 152, 113, 153, 114, 154, 115, 155, 116, 156, 117, 157, 118, 158, 119, 159, 120, 160)
d3: (12, 32)(51, 121)(52, 142)(71, 141)(72, 122)(82, 102)
e3: (10, 30)(49, 159)(50, 140)(69, 139)(70, 160)(100, 120)
f3: (11, 31)(50, 160)(51, 141)(70, 140)(71, 121)(81, 101)
g3: (8, 98)(28, 118)(47, 157)(67, 137)
h3: (9, 29)(48, 158)(49, 139)(68, 138)(69, 159)(99, 119)
m3: (20, 40)(59, 129)(60, 150)(79, 149)(80, 130)(90, 110)

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

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