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On this page are computer-accessible forms for the graph C4[ 160, 67 ] = SDD(MPS(4,20;3)).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {76, 108} under the group generated by the following permutations:

a: (90, 130)
b: (98, 138)
c: (113, 153)
d: (109, 149)
e: (81, 121)
f: (99, 139)
g: (105, 145)
h: (84, 124)
m: (110, 150)
n1: (88, 128)
a1: (106, 146)
b1: (103, 143)
c1: (112, 152)
d1: (2, 5)(3, 42)(4, 41)(6, 38)(7, 60)(8, 59)(9, 37)(10, 34)(11, 57)(12, 58)(13, 33)(14, 30)(15, 56)(16, 55)(17, 29)(18, 26)(19, 54)(20, 53)(21, 25)(23, 52)(24, 51)(27, 50)(28, 49)(31, 48)(32, 47)(35, 46)(36, 45)(39, 43)(40, 44)(61, 73)(62, 71)(63, 72)(64, 70)(65, 69)(66, 68)(74, 80)(75, 79)(76, 78)(81, 91)(82, 100)(83, 99)(84, 98)(85, 97)(86, 96)(87, 95)(88, 94)(89, 93)(90, 92)(101, 111)(102, 120)(103, 119)(104, 118)(105, 117)(106, 116)(107, 115)(108, 114)(109, 113)(110, 112)(121, 131)(122, 140)(123, 139)(124, 138)(125, 137)(126, 136)(127, 135)(128, 134)(129, 133)(130, 132)(141, 151)(142, 160)(143, 159)(144, 158)(145, 157)(146, 156)(147, 155)(148, 154)(149, 153)(150, 152)
e1: (108, 148)
f1: (86, 126)
g1: (97, 137)
h1: (100, 140)
m1: (118, 158)
n2: (104, 144)
a2: (89, 129)
b2: (119, 159)
c2: (101, 141)
d2: (93, 133)
e2: (111, 151)
f2: (102, 142)
g2: (95, 135)
h2: (115, 155)
m2: (1, 2)(3, 4)(5, 38)(6, 37)(7, 40)(8, 39)(9, 34)(10, 33)(11, 36)(12, 35)(13, 30)(14, 29)(15, 32)(16, 31)(17, 26)(18, 25)(19, 28)(20, 27)(21, 22)(23, 24)(41, 60)(42, 59)(43, 57)(44, 58)(45, 56)(46, 55)(47, 54)(48, 53)(49, 52)(50, 51)(61, 62)(63, 80)(64, 79)(65, 78)(66, 77)(67, 76)(68, 75)(69, 74)(70, 73)(71, 72)(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)
n3: (91, 131)
a3: (120, 160)
b3: (107, 147)
c3: (1, 3, 2, 4)(5, 15, 38, 32)(6, 16, 37, 31)(7, 13, 40, 30)(8, 14, 39, 29)(9, 27, 34, 20)(10, 28, 33, 19)(11, 26, 36, 17)(12, 25, 35, 18)(21, 23, 22, 24)(41, 74, 60, 69)(42, 75, 59, 68)(43, 61, 57, 62)(44, 80, 58, 63)(45, 67, 56, 76)(46, 66, 55, 77)(47, 73, 54, 70)(48, 71, 53, 72)(49, 79, 52, 64)(50, 78, 51, 65)(82, 84, 90, 88)(83, 87, 89, 85)(91, 112, 100, 119)(92, 115, 99, 116)(93, 118, 98, 113)(94, 111, 97, 120)(95, 114, 96, 117)(102, 104, 110, 108)(103, 107, 109, 105)(122, 124, 130, 128)(123, 127, 129, 125)(131, 152, 140, 159)(132, 155, 139, 156)(133, 158, 138, 153)(134, 151, 137, 160)(135, 154, 136, 157)(142, 144, 150, 148)(143, 147, 149, 145)
d3: (92, 132)
e3: (96, 136)
f3: (83, 123)
g3: (82, 122)
h3: (116, 156)
m3: (114, 154)
n4: (85, 125)
a4: (94, 134)
b4: (117, 157)

(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.

**************

&Graph
C4[ 160, 67 ]
160
-1 121 91 81 131
-2 121 100 81 140
-3 121 112 81 152
-4 121 81 159 119
-5 122 91 82 131
-6 132 122 92 82
-7 122 113 82 153
-8 122 82 160 120
-9 132 123 92 83
-10 133 123 93 83
-11 111 123 83 151
-12 154 123 114 83
-13 133 124 93 84
-14 134 124 94 84
-15 112 124 84 152
-16 155 124 115 84
-17 134 125 94 85
-18 135 125 95 85
-19 113 125 85 153
-20 156 125 116 85
-21 135 126 95 86
-22 136 126 96 86
-23 154 114 126 86
-24 157 126 117 86
-25 136 127 96 87
-26 137 127 97 87
-27 155 115 127 87
-28 158 127 118 87
-29 88 137 128 97
-30 88 138 128 98
-31 88 156 116 128
-32 88 159 128 119
-33 89 138 129 98
-34 99 89 139 129
-35 89 157 117 129
-36 89 160 129 120
-37 99 90 139 130
-38 100 90 140 130
-39 111 90 151 130
-40 90 158 118 130
-41 143 91 103 131
-42 110 91 150 131
-43 132 101 92 141
-44 132 144 92 104
-45 133 102 93 142
-46 133 145 93 105
-47 143 134 103 94
-48 134 146 94 106
-49 144 135 104 95
-50 135 147 95 107
-51 145 136 105 96
-52 136 148 96 108
-53 146 137 106 97
-54 137 149 97 109
-55 147 138 107 98
-56 110 138 150 98
-57 99 101 139 141
-58 99 148 139 108
-59 100 102 140 142
-60 100 149 140 109
-61 155 101 115 141
-62 101 156 116 141
-63 156 102 116 142
-64 102 157 117 142
-65 143 157 103 117
-66 143 103 158 118
-67 144 158 104 118
-68 144 104 159 119
-69 145 159 105 119
-70 145 105 160 120
-71 111 146 106 151
-72 146 160 106 120
-73 111 147 107 151
-74 112 147 107 152
-75 112 148 108 152
-76 113 148 108 153
-77 113 149 109 153
-78 154 114 149 109
-79 110 154 114 150
-80 110 155 115 150
-81 1 2 3 4
-82 5 6 7 8
-83 11 12 9 10
-84 13 14 15 16
-85 17 18 19 20
-86 22 23 24 21
-87 25 26 27 28
-88 29 30 31 32
-89 33 34 35 36
-90 37 38 39 40
-91 1 5 41 42
-92 44 6 9 43
-93 45 13 46 10
-94 14 47 48 17
-95 49 50 18 21
-96 22 25 51 52
-97 26 29 53 54
-98 33 55 56 30
-99 34 57 58 37
-100 2 59 38 60
-101 57 61 62 43
-102 45 59 63 64
-103 66 47 41 65
-104 44 67 68 49
-105 46 69 70 51
-106 48 71 72 53
-107 55 50 73 74
-108 58 52 75 76
-109 77 78 60 54
-110 56 79 80 42
-111 11 71 39 73
-112 3 15 74 75
-113 77 7 19 76
-114 12 23 78 79
-115 80 16 27 61
-116 62 63 20 31
-117 24 35 64 65
-118 66 67 28 40
-119 68 69 4 32
-120 36 70 72 8
-121 1 2 3 4
-122 5 6 7 8
-123 11 12 9 10
-124 13 14 15 16
-125 17 18 19 20
-126 22 23 24 21
-127 25 26 27 28
-128 29 30 31 32
-129 33 34 35 36
-130 37 38 39 40
-131 1 5 41 42
-132 44 6 9 43
-133 45 13 46 10
-134 14 47 48 17
-135 49 50 18 21
-136 22 25 51 52
-137 26 29 53 54
-138 33 55 56 30
-139 34 57 58 37
-140 2 59 38 60
-141 57 61 62 43
-142 45 59 63 64
-143 66 47 41 65
-144 44 67 68 49
-145 46 69 70 51
-146 48 71 72 53
-147 55 50 73 74
-148 58 52 75 76
-149 77 78 60 54
-150 56 79 80 42
-151 11 71 39 73
-152 3 15 74 75
-153 77 7 19 76
-154 12 23 78 79
-155 80 16 27 61
-156 62 63 20 31
-157 24 35 64 65
-158 66 67 28 40
-159 68 69 4 32
-160 36 70 72 8
0

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