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On this page are computer-accessible forms for the graph C4[ 160, 76 ] = SS[160,19].

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {1, 3} under the group generated by the following permutations:

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

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

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

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