[Home] [Table] [Glossary] [Families]

On this page are computer-accessible forms for the graph C4[ 164, 5 ] = SDD(C_41(1,9)).

(I) Following is a form readable by MAGMA:

g:=Graph<164|{ {80, 120}, {82, 122}, {81, 121}, {80, 121}, {82, 123}, {68, 111}, {81, 122}, {66, 110}, {67, 111}, {64, 109}, {65, 111}, {65, 110}, {74, 123}, {72, 122}, {67, 112}, {69, 113}, {66, 119}, {71, 114}, {69, 112}, {64, 118}, {71, 113}, {70, 112}, {79, 120}, {74, 114}, {79, 119}, {78, 118}, {77, 117}, {76, 116}, {75, 115}, {72, 113}, {78, 119}, {76, 117}, {73, 115}, {73, 114}, {77, 118}, {68, 120}, {70, 121}, {75, 116}, {27, 91}, {29, 93}, {44, 108}, {26, 91}, {31, 94}, {29, 92}, {42, 107}, {24, 90}, {31, 93}, {30, 92}, {40, 106}, {25, 90}, {35, 96}, {46, 109}, {37, 97}, {52, 112}, {34, 103}, {39, 98}, {37, 96}, {26, 92}, {39, 97}, {38, 96}, {32, 102}, {16, 87}, {28, 91}, {54, 113}, {17, 89}, {60, 116}, {42, 98}, {43, 99}, {45, 101}, {17, 88}, {58, 115}, {40, 97}, {45, 100}, {47, 102}, {18, 88}, {41, 99}, {46, 100}, {47, 101}, {56, 114}, {19, 88}, {62, 117}, {41, 98}, {21, 89}, {36, 104}, {23, 91}, {20, 89}, {23, 90}, {20, 90}, {22, 89}, {38, 105}, {43, 100}, {44, 99}, {3, 83}, {61, 109}, {59, 107}, {58, 106}, {5, 85}, {2, 83}, {63, 110}, {61, 108}, {5, 84}, {56, 105}, {1, 83}, {63, 109}, {62, 108}, {57, 107}, {6, 84}, {7, 84}, {57, 106}, {12, 95}, {52, 103}, {50, 102}, {51, 103}, {1, 84}, {48, 101}, {14, 88}, {49, 103}, {4, 83}, {60, 107}, {59, 108}, {9, 94}, {49, 102}, {15, 87}, {14, 87}, {12, 86}, {6, 93}, {13, 86}, {51, 104}, {9, 85}, {11, 87}, {53, 105}, {8, 85}, {11, 86}, {50, 111}, {53, 104}, {55, 106}, {2, 92}, {8, 86}, {48, 110}, {54, 104}, {55, 105}, {10, 85}, {25, 122}, {16, 119}, {28, 123}, {19, 120}, {15, 96}, {22, 121}, {3, 115}, {13, 127}, {7, 116}, {18, 97}, {12, 127}, {10, 126}, {11, 127}, {8, 126}, {8, 127}, {21, 98}, {9, 126}, {4, 124}, {5, 125}, {7, 125}, {5, 126}, {36, 95}, {30, 101}, {24, 99}, {13, 118}, {6, 125}, {1, 125}, {35, 95}, {34, 94}, {1, 124}, {32, 93}, {2, 124}, {33, 95}, {3, 124}, {33, 94}, {27, 100}, {10, 117}, {4, 123}, {6, 134}, {12, 136}, {15, 137}, {2, 133}, {11, 128}, {9, 135}, {14, 128}, {14, 129}, {15, 128}, {16, 128}, {30, 142}, {17, 129}, {13, 159}, {19, 129}, {17, 130}, {23, 132}, {18, 129}, {10, 158}, {24, 140}, {23, 131}, {22, 130}, {20, 130}, {27, 141}, {20, 131}, {21, 130}, {18, 138}, {31, 135}, {29, 133}, {28, 132}, {31, 134}, {7, 157}, {25, 131}, {24, 131}, {30, 133}, {29, 134}, {21, 139}, {26, 132}, {3, 156}, {27, 132}, {26, 133}, {4, 164}, {62, 158}, {44, 140}, {45, 141}, {47, 143}, {42, 139}, {60, 157}, {47, 142}, {49, 144}, {40, 138}, {41, 139}, {51, 145}, {45, 142}, {56, 155}, {46, 141}, {51, 144}, {52, 144}, {53, 145}, {55, 147}, {34, 135}, {41, 140}, {55, 146}, {32, 134}, {58, 156}, {33, 135}, {43, 141}, {43, 140}, {48, 151}, {53, 146}, {54, 145}, {60, 148}, {63, 151}, {61, 149}, {33, 136}, {63, 150}, {58, 147}, {35, 137}, {57, 147}, {56, 146}, {50, 152}, {35, 136}, {62, 149}, {61, 150}, {36, 136}, {39, 139}, {37, 137}, {54, 154}, {39, 138}, {57, 148}, {52, 153}, {59, 149}, {32, 143}, {59, 148}, {38, 137}, {37, 138}, {16, 160}, {19, 161}, {34, 144}, {22, 162}, {38, 146}, {36, 145}, {28, 164}, {46, 150}, {44, 149}, {25, 163}, {40, 147}, {50, 143}, {42, 148}, {48, 142}, {49, 143}, {74, 155}, {78, 159}, {76, 157}, {72, 154}, {77, 159}, {76, 158}, {73, 155}, {77, 158}, {66, 151}, {73, 156}, {64, 150}, {75, 157}, {65, 151}, {75, 156}, {65, 152}, {67, 153}, {67, 152}, {68, 152}, {71, 155}, {69, 153}, {71, 154}, {64, 159}, {70, 153}, {69, 154}, {66, 160}, {70, 162}, {68, 161}, {72, 163}, {74, 164}, {79, 161}, {78, 160}, {79, 160}, {80, 161}, {82, 163}, {80, 162}, {81, 163}, {81, 162}, {82, 164} }>;

(II) A more general form is to represent the graph as the orbit of {80, 120} under the group generated by the following permutations:

a: (91, 132)
b: (104, 145)
c: (122, 163)
d: (117, 158)
e: (98, 139)
f: (112, 153)
g: (123, 164)
h: (95, 136)
m: (101, 142)
n1: (116, 157)
a1: (97, 138)
b1: (120, 161)
c1: (109, 150)
d1: (87, 128)
e1: (88, 129)
f1: (107, 148)
g1: (2, 7)(3, 6)(4, 5)(8, 82)(9, 74)(10, 28)(11, 81)(12, 72)(13, 25)(14, 80)(15, 70)(16, 22)(17, 79)(18, 68)(20, 78)(21, 66)(23, 77)(24, 64)(26, 76)(27, 62)(29, 75)(30, 60)(31, 73)(32, 58)(33, 71)(34, 56)(35, 69)(36, 54)(37, 67)(38, 52)(39, 65)(40, 50)(41, 63)(42, 48)(43, 61)(44, 46)(45, 59)(47, 57)(49, 55)(51, 53)(83, 84)(85, 123)(86, 122)(87, 121)(88, 120)(89, 119)(90, 118)(91, 117)(92, 116)(93, 115)(94, 114)(95, 113)(96, 112)(97, 111)(98, 110)(99, 109)(100, 108)(101, 107)(102, 106)(103, 105)(124, 125)(126, 164)(127, 163)(128, 162)(129, 161)(130, 160)(131, 159)(132, 158)(133, 157)(134, 156)(135, 155)(136, 154)(137, 153)(138, 152)(139, 151)(140, 150)(141, 149)(142, 148)(143, 147)(144, 146)
h1: (92, 133)
m1: (102, 143)
n2: (119, 160)
a2: (114, 155)
b2: (94, 135)
c2: (84, 125)
d2: (111, 152)
e2: (1, 2, 29, 6)(3, 26, 32, 5)(4, 30, 31, 7)(8, 58, 23, 50)(9, 75, 28, 47)(10, 73, 27, 49)(11, 40, 20, 68)(12, 57, 25, 65)(13, 55, 24, 67)(14, 18, 17, 19)(15, 39, 22, 79)(16, 37, 21, 80)(33, 60, 82, 48)(34, 76, 74, 45)(35, 42, 81, 66)(36, 59, 72, 63)(38, 41, 70, 78)(43, 52, 77, 56)(44, 69, 64, 53)(46, 51, 62, 71)(54, 61)(83, 92, 93, 84)(85, 115, 91, 102)(86, 106, 90, 111)(87, 97, 89, 120)(94, 116, 123, 101)(95, 107, 122, 110)(96, 98, 121, 119)(99, 112, 118, 105)(100, 103, 117, 114)(104, 108, 113, 109)(124, 133, 134, 125)(126, 156, 132, 143)(127, 147, 131, 152)(128, 138, 130, 161)(135, 157, 164, 142)(136, 148, 163, 151)(137, 139, 162, 160)(140, 153, 159, 146)(141, 144, 158, 155)(145, 149, 154, 150)
f2: (106, 147)
g2: (113, 154)
h2: (100, 141)
m2: (115, 156)
n3: (93, 134)
a3: (90, 131)
b3: (108, 149)
c3: (99, 140)
d3: (121, 162)
e3: (110, 151)
f3: (103, 144)
g3: (118, 159)
h3: (89, 130)
m3: (105, 146)
n4: (83, 124)
a4: (86, 127)
b4: (85, 126)

(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[ 164, 5 ]
164
-1 124 125 83 84
-2 133 124 92 83
-3 156 124 115 83
-4 123 124 83 164
-5 125 126 84 85
-6 134 125 93 84
-7 157 125 116 84
-8 126 127 85 86
-9 135 126 94 85
-10 158 126 117 85
-11 127 128 86 87
-12 136 127 95 86
-13 159 127 118 86
-14 88 128 129 87
-15 137 128 96 87
-16 160 128 119 87
-17 88 89 129 130
-18 88 138 129 97
-19 88 161 129 120
-20 89 90 130 131
-21 89 139 130 98
-22 121 89 162 130
-23 132 90 91 131
-24 99 90 140 131
-25 122 90 163 131
-26 132 133 91 92
-27 132 100 91 141
-28 132 123 91 164
-29 133 134 92 93
-30 133 101 92 142
-31 134 135 93 94
-32 143 134 102 93
-33 135 136 94 95
-34 144 135 103 94
-35 136 137 95 96
-36 145 136 104 95
-37 137 138 96 97
-38 146 137 105 96
-39 138 139 97 98
-40 147 138 106 97
-41 99 139 140 98
-42 148 139 107 98
-43 99 100 140 141
-44 99 149 140 108
-45 100 101 141 142
-46 100 150 141 109
-47 143 101 102 142
-48 110 101 151 142
-49 143 144 102 103
-50 143 111 102 152
-51 144 145 103 104
-52 144 112 103 153
-53 145 146 104 105
-54 154 145 113 104
-55 146 147 105 106
-56 155 146 114 105
-57 147 148 106 107
-58 156 147 115 106
-59 148 149 107 108
-60 157 148 116 107
-61 149 150 108 109
-62 158 149 117 108
-63 110 150 151 109
-64 159 150 118 109
-65 110 111 151 152
-66 110 160 151 119
-67 111 112 152 153
-68 111 161 152 120
-69 154 112 113 153
-70 121 112 162 153
-71 154 155 113 114
-72 154 122 113 163
-73 155 156 114 115
-74 155 123 114 164
-75 156 157 115 116
-76 157 158 116 117
-77 158 159 117 118
-78 159 160 118 119
-79 160 161 119 120
-80 121 161 162 120
-81 121 122 162 163
-82 122 123 163 164
-83 1 2 3 4
-84 1 5 6 7
-85 5 8 9 10
-86 11 12 13 8
-87 11 14 15 16
-88 14 17 18 19
-89 22 17 20 21
-90 23 24 25 20
-91 23 26 27 28
-92 2 26 29 30
-93 6 29 31 32
-94 33 34 9 31
-95 33 12 35 36
-96 35 15 37 38
-97 37 39 18 40
-98 39 41 42 21
-99 44 24 41 43
-100 45 46 27 43
-101 45 47 48 30
-102 47 49 50 32
-103 34 49 51 52
-104 36 51 53 54
-105 55 56 38 53
-106 55 57 58 40
-107 57 59 60 42
-108 44 59 61 62
-109 46 61 63 64
-110 66 48 63 65
-111 67 68 50 65
-112 67 69 70 52
-113 69 71 72 54
-114 56 71 73 74
-115 3 58 73 75
-116 60 7 75 76
-117 77 62 10 76
-118 77 78 13 64
-119 66 78 79 16
-120 68 79 80 19
-121 22 80 70 81
-122 25 81 82 72
-123 4 82 28 74
-124 1 2 3 4
-125 1 5 6 7
-126 5 8 9 10
-127 11 12 13 8
-128 11 14 15 16
-129 14 17 18 19
-130 22 17 20 21
-131 23 24 25 20
-132 23 26 27 28
-133 2 26 29 30
-134 6 29 31 32
-135 33 34 9 31
-136 33 12 35 36
-137 35 15 37 38
-138 37 39 18 40
-139 39 41 42 21
-140 44 24 41 43
-141 45 46 27 43
-142 45 47 48 30
-143 47 49 50 32
-144 34 49 51 52
-145 36 51 53 54
-146 55 56 38 53
-147 55 57 58 40
-148 57 59 60 42
-149 44 59 61 62
-150 46 61 63 64
-151 66 48 63 65
-152 67 68 50 65
-153 67 69 70 52
-154 69 71 72 54
-155 56 71 73 74
-156 3 58 73 75
-157 60 7 75 76
-158 77 62 10 76
-159 77 78 13 64
-160 66 78 79 16
-161 68 79 80 19
-162 22 80 70 81
-163 25 81 82 72
-164 4 82 28 74
0

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