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On this page are computer-accessible forms for the graph C4[ 132, 5 ] = R_66(35,34).

(I) Following is a form readable by MAGMA:

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

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

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

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