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

On this page are computer-accessible forms for the graph C4[ 136, 15 ] = SDD(C_34(1,13)).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {64, 97} under the group generated by the following permutations:

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

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

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