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

On this page are computer-accessible forms for the graph C4[ 168, 56 ] = SDD(C_42(1,13)).

(I) Following is a form readable by MAGMA:

g:=Graph<168|{ {80, 87}, {75, 89}, {79, 90}, {65, 86}, {77, 90}, {75, 92}, {77, 85}, {71, 93}, {77, 87}, {77, 86}, {75, 85}, {67, 92}, {65, 97}, {79, 111}, {74, 104}, {74, 111}, {65, 105}, {75, 99}, {80, 121}, {67, 105}, {83, 121}, {64, 107}, {74, 97}, {71, 108}, {76, 99}, {69, 117}, {80, 98}, {73, 125}, {78, 120}, {74, 125}, {65, 120}, {70, 124}, {80, 106}, {81, 106}, {82, 110}, {42, 107}, {36, 102}, {35, 102}, {37, 96}, {54, 113}, {23, 95}, {62, 118}, {58, 115}, {60, 117}, {61, 118}, {48, 124}, {35, 109}, {50, 124}, {16, 95}, {39, 119}, {60, 108}, {42, 122}, {45, 125}, {38, 119}, {43, 122}, {4, 86}, {33, 115}, {32, 114}, {15, 93}, {14, 92}, {11, 89}, {5, 87}, {50, 96}, {1, 85}, {37, 113}, {37, 112}, {50, 103}, {1, 87}, {62, 104}, {34, 116}, {13, 91}, {12, 90}, {46, 120}, {47, 121}, {1, 86}, {8, 95}, {2, 85}, {41, 126}, {44, 123}, {3, 91}, {35, 123}, {6, 94}, {43, 115}, {44, 116}, {7, 94}, {60, 101}, {34, 123}, {1, 90}, {33, 122}, {3, 88}, {2, 89}, {36, 127}, {37, 126}, {41, 114}, {54, 109}, {50, 110}, {56, 100}, {57, 100}, {2, 92}, {32, 126}, {6, 88}, {3, 93}, {58, 101}, {61, 98}, {16, 112}, {17, 113}, {2, 99}, {21, 116}, {19, 114}, {17, 112}, {57, 88}, {7, 101}, {60, 94}, {10, 104}, {57, 91}, {12, 111}, {28, 127}, {22, 117}, {18, 113}, {15, 108}, {57, 93}, {61, 89}, {4, 97}, {10, 111}, {8, 109}, {3, 100}, {23, 112}, {21, 114}, {20, 115}, {19, 116}, {14, 105}, {9, 110}, {5, 98}, {9, 96}, {11, 98}, {21, 127}, {7, 108}, {10, 97}, {19, 127}, {4, 105}, {6, 107}, {8, 102}, {25, 119}, {24, 118}, {9, 103}, {5, 106}, {17, 126}, {24, 104}, {17, 96}, {31, 110}, {20, 101}, {7, 117}, {21, 103}, {42, 88}, {8, 123}, {19, 103}, {42, 94}, {9, 124}, {30, 107}, {10, 125}, {29, 106}, {26, 99}, {13, 119}, {28, 102}, {4, 120}, {35, 95}, {6, 122}, {5, 121}, {39, 91}, {11, 118}, {18, 109}, {27, 100}, {27, 155}, {22, 148}, {31, 157}, {30, 156}, {27, 153}, {26, 152}, {12, 143}, {16, 147}, {23, 147}, {33, 165}, {11, 142}, {28, 154}, {29, 155}, {36, 162}, {26, 157}, {40, 160}, {13, 132}, {29, 148}, {15, 134}, {46, 164}, {14, 133}, {45, 166}, {45, 161}, {24, 149}, {43, 165}, {46, 160}, {47, 161}, {12, 131}, {23, 135}, {27, 139}, {26, 138}, {24, 138}, {25, 139}, {52, 166}, {53, 167}, {55, 165}, {59, 168}, {20, 128}, {51, 167}, {20, 130}, {49, 167}, {16, 135}, {63, 168}, {31, 136}, {22, 129}, {25, 129}, {49, 168}, {18, 136}, {30, 132}, {25, 130}, {59, 167}, {63, 163}, {13, 144}, {63, 162}, {15, 146}, {29, 131}, {14, 145}, {22, 137}, {18, 141}, {49, 144}, {56, 153}, {39, 132}, {45, 142}, {56, 155}, {38, 130}, {55, 147}, {40, 141}, {41, 140}, {52, 146}, {38, 129}, {48, 152}, {47, 134}, {63, 150}, {51, 154}, {53, 158}, {62, 149}, {59, 144}, {55, 156}, {32, 140}, {38, 139}, {51, 158}, {48, 159}, {53, 154}, {49, 128}, {53, 135}, {44, 159}, {61, 142}, {56, 139}, {51, 135}, {62, 138}, {34, 151}, {43, 158}, {48, 133}, {32, 150}, {47, 153}, {39, 144}, {58, 130}, {40, 145}, {58, 128}, {31, 164}, {59, 128}, {44, 151}, {46, 149}, {52, 143}, {54, 141}, {55, 140}, {30, 163}, {34, 159}, {52, 137}, {28, 162}, {36, 154}, {54, 136}, {33, 158}, {40, 151}, {41, 150}, {79, 143}, {71, 134}, {70, 133}, {64, 132}, {69, 129}, {72, 141}, {81, 148}, {67, 133}, {84, 146}, {76, 138}, {73, 142}, {81, 155}, {83, 153}, {69, 137}, {79, 131}, {66, 140}, {82, 157}, {66, 147}, {76, 157}, {69, 148}, {67, 145}, {81, 131}, {68, 150}, {76, 152}, {71, 146}, {83, 134}, {70, 159}, {72, 145}, {82, 136}, {78, 149}, {84, 143}, {64, 156}, {84, 137}, {66, 156}, {70, 152}, {72, 151}, {64, 163}, {68, 162}, {66, 165}, {68, 163}, {72, 160}, {73, 161}, {78, 164}, {68, 168}, {78, 160}, {73, 166}, {83, 161}, {84, 166}, {82, 164} }>;

(II) A more general form is to represent the graph as the orbit of {80, 87} under the group generated by the following permutations:

a: (3, 57)
b: (40, 72)
c: (32, 41)
d: (16, 23)
e: (15, 71)
f: (12, 79)
g: (18, 54)
h: (11, 61)
m: (47, 83)
n1: (9, 50)
a1: (22, 69)
b1: (30, 64)
c1: (51, 53)
d1: (33, 43)
e1: (14, 67)
f1: (25, 38)
g1: (6, 42)
h1: (27, 56)
m1: (7, 60)
n2: (2, 4)(3, 7)(5, 12)(8, 19)(9, 18)(10, 11)(13, 20)(16, 32)(21, 35)(22, 27)(23, 41)(26, 46)(30, 33)(39, 58)(40, 48)(43, 64)(47, 52)(50, 54)(51, 63)(53, 68)(56, 69)(57, 60)(61, 74)(65, 75)(70, 72)(76, 78)(79, 80)(83, 84)(85, 86)(87, 90)(88, 94)(89, 97)(91, 101)(92, 105)(93, 108)(95, 114)(96, 113)(98, 111)(99, 120)(100, 117)(102, 127)(103, 109)(104, 118)(106, 131)(107, 122)(110, 136)(112, 126)(115, 132)(116, 123)(119, 130)(121, 143)(124, 141)(125, 142)(128, 144)(129, 139)(133, 145)(134, 146)(135, 150)(137, 153)(138, 149)(140, 147)(148, 155)(151, 159)(152, 160)(154, 162)(156, 165)(157, 164)(158, 163)(161, 166)(167, 168)
a2: (2, 75)
b2: (19, 21)
c2: (17, 37)
d2: (24, 62)
e2: (45, 73)
f2: (29, 81)
g2: (8, 35)
h2: (49, 59)
m2: (31, 82)
n3: (4, 65)
a3: (34, 44)
b3: (63, 68)
c3: (10, 74)
d3: (46, 78)
e3: (2, 12)(3, 18)(4, 5)(6, 17)(7, 9)(8, 13)(10, 11)(14, 29)(15, 31)(16, 30)(19, 20)(21, 58)(22, 48)(23, 64)(24, 45)(25, 34)(26, 52)(27, 40)(28, 49)(32, 33)(35, 39)(36, 59)(37, 42)(38, 44)(41, 43)(46, 47)(50, 60)(51, 63)(53, 68)(54, 57)(56, 72)(61, 74)(62, 73)(65, 80)(67, 81)(69, 70)(71, 82)(75, 79)(76, 84)(78, 83)(85, 90)(86, 87)(88, 113)(89, 111)(91, 109)(92, 131)(93, 136)(94, 96)(95, 132)(97, 98)(99, 143)(100, 141)(101, 103)(102, 144)(104, 142)(105, 106)(107, 112)(108, 110)(114, 115)(116, 130)(117, 124)(118, 125)(119, 123)(120, 121)(122, 126)(127, 128)(129, 159)(133, 148)(134, 164)(135, 163)(137, 152)(138, 166)(139, 151)(140, 165)(145, 155)(146, 157)(147, 156)(149, 161)(150, 158)(153, 160)(154, 168)(162, 167)
f3: (26, 76)
g3: (13, 39)
h3: (20, 58)
m3: (5, 80)
n4: (55, 66)
a4: (48, 70)
b4: (52, 84)
c4: (28, 36)
d4: (1, 2)(3, 8)(4, 11)(5, 14)(6, 16)(7, 17)(9, 22)(10, 24)(12, 26)(13, 28)(15, 18)(19, 25)(20, 32)(21, 38)(23, 42)(27, 34)(29, 48)(30, 51)(31, 52)(33, 55)(35, 57)(36, 39)(37, 60)(40, 47)(41, 58)(43, 66)(44, 56)(45, 46)(49, 63)(50, 69)(53, 64)(54, 71)(59, 68)(61, 65)(62, 74)(67, 80)(70, 81)(72, 83)(73, 78)(75, 77)(76, 79)(82, 84)(86, 89)(87, 92)(88, 95)(90, 99)(91, 102)(93, 109)(94, 112)(96, 117)(97, 118)(98, 105)(100, 123)(101, 126)(103, 129)(106, 133)(107, 135)(108, 113)(110, 137)(111, 138)(114, 130)(115, 140)(116, 139)(119, 127)(120, 142)(121, 145)(122, 147)(124, 148)(125, 149)(128, 150)(131, 152)(132, 154)(134, 141)(136, 146)(143, 157)(144, 162)(151, 153)(155, 159)(156, 158)(160, 161)(163, 167)(164, 166)

(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[ 168, 56 ]
168
-1 90 85 86 87
-2 99 89 92 85
-3 88 100 91 93
-4 105 86 97 120
-5 121 106 87 98
-6 88 122 94 107
-7 101 94 117 108
-8 123 102 95 109
-9 110 124 103 96
-10 111 125 104 97
-11 89 118 98 142
-12 143 111 90 131
-13 132 144 91 119
-14 133 145 92 105
-15 134 146 93 108
-16 112 135 147 95
-17 112 113 126 96
-18 113 136 141 109
-19 103 114 116 127
-20 101 115 128 130
-21 103 114 116 127
-22 137 148 117 129
-23 112 135 147 95
-24 104 138 149 118
-25 139 129 119 130
-26 99 157 138 152
-27 100 155 139 153
-28 154 102 127 162
-29 155 148 106 131
-30 132 156 107 163
-31 110 157 136 164
-32 114 126 150 140
-33 165 122 158 115
-34 123 159 116 151
-35 123 102 95 109
-36 154 102 127 162
-37 112 113 126 96
-38 139 129 119 130
-39 132 144 91 119
-40 145 160 151 141
-41 114 126 150 140
-42 88 122 94 107
-43 165 122 158 115
-44 123 159 116 151
-45 166 125 161 142
-46 149 160 120 164
-47 121 134 161 153
-48 133 124 159 152
-49 144 167 168 128
-50 110 124 103 96
-51 154 167 135 158
-52 143 166 146 137
-53 154 167 135 158
-54 113 136 141 109
-55 165 156 147 140
-56 100 155 139 153
-57 88 100 91 93
-58 101 115 128 130
-59 144 167 168 128
-60 101 94 117 108
-61 89 118 98 142
-62 104 138 149 118
-63 168 150 162 163
-64 132 156 107 163
-65 105 86 97 120
-66 165 156 147 140
-67 133 145 92 105
-68 168 150 162 163
-69 137 148 117 129
-70 133 124 159 152
-71 134 146 93 108
-72 145 160 151 141
-73 166 125 161 142
-74 111 125 104 97
-75 99 89 92 85
-76 99 157 138 152
-77 90 85 86 87
-78 149 160 120 164
-79 143 111 90 131
-80 121 106 87 98
-81 155 148 106 131
-82 110 157 136 164
-83 121 134 161 153
-84 143 166 146 137
-85 77 1 2 75
-86 77 1 4 65
-87 77 1 80 5
-88 57 3 6 42
-89 11 2 61 75
-90 77 1 12 79
-91 13 57 3 39
-92 67 2 14 75
-93 57 3 15 71
-94 60 6 7 42
-95 23 35 16 8
-96 37 17 50 9
-97 4 74 10 65
-98 11 80 5 61
-99 2 26 75 76
-100 56 57 3 27
-101 58 60 7 20
-102 35 36 28 8
-103 50 19 9 21
-104 24 62 74 10
-105 67 14 4 65
-106 80 81 5 29
-107 6 30 42 64
-108 15 60 71 7
-109 35 18 8 54
-110 82 50 9 31
-111 12 79 74 10
-112 23 37 16 17
-113 37 17 18 54
-114 19 41 21 32
-115 33 58 20 43
-116 44 34 19 21
-117 22 69 60 7
-118 11 24 61 62
-119 13 25 38 39
-120 78 46 4 65
-121 47 80 5 83
-122 33 6 42 43
-123 44 34 35 8
-124 48 70 50 9
-125 45 73 74 10
-126 37 17 41 32
-127 36 28 19 21
-128 58 59 49 20
-129 22 25 69 38
-130 25 58 38 20
-131 12 79 81 29
-132 13 39 30 64
-133 67 14 48 70
-134 47 15 71 83
-135 23 16 51 53
-136 82 18 31 54
-137 22 69 84 52
-138 24 26 62 76
-139 56 25 27 38
-140 55 66 41 32
-141 72 18 40 54
-142 11 45 61 73
-143 12 79 84 52
-144 13 59 49 39
-145 67 14 72 40
-146 15 71 84 52
-147 55 66 23 16
-148 22 69 81 29
-149 78 24 46 62
-150 68 41 63 32
-151 44 34 72 40
-152 26 48 70 76
-153 56 47 27 83
-154 36 28 51 53
-155 56 81 27 29
-156 55 66 30 64
-157 26 82 31 76
-158 33 51 53 43
-159 44 34 48 70
-160 78 46 72 40
-161 45 47 83 73
-162 68 36 28 63
-163 68 30 63 64
-164 78 46 82 31
-165 33 55 66 43
-166 45 73 84 52
-167 59 49 51 53
-168 68 59 49 63
0

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