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

On this page are computer-accessible forms for the graph C4[ 116, 3 ] = R_58(31,30).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {2, 3} under the group generated by the following permutations:

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

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

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