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On this page are computer-accessible forms for the graph C4[ 136, 1 ] = W(68,2).

(I) Following is a form readable by MAGMA:

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

(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: (18, 86)
b: (49, 117)
c: (59, 127)
d: (28, 96)
e: (58, 126)
f: (27, 95)
g: (66, 134)
h: (68, 136)
m: (30, 98)
n1: (57, 125)
a1: (26, 94)
b1: (12, 80)
c1: (43, 111)
d1: (61, 129)
e1: (53, 121)
f1: (46, 114)
g1: (15, 83)
h1: (22, 90)
m1: (9, 77)
n2: (44, 112)
a2: (65, 133)
b2: (29, 97)
c2: (52, 120)
d2: (17, 85)
e2: (2, 70)
f2: (54, 122)
g2: (31, 99)
h2: (23, 91)
m2: (16, 84)
n3: (47, 115)
a3: (4, 72)
b3: (35, 103)
c3: (21, 89)
d3: (56, 124)
e3: (60, 128)
f3: (25, 93)
g3: (51, 119)
h3: (20, 88)
m3: (3, 71)
n4: (34, 102)
a4: (55, 123)
b4: (24, 92)
c4: (13, 81)
d4: (48, 116)
e4: (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, 133, 134, 135, 136)
f4: (10, 78)
g4: (41, 109)
h4: (67, 135)
m4: (36, 104)
n5: (8, 76)
a5: (39, 107)
b5: (5, 73)
c5: (40, 108)
d5: (64, 132)
e5: (14, 82)
f5: (45, 113)
g5: (32, 100)
h5: (11, 79)
m5: (42, 110)
n6: (7, 75)
a6: (38, 106)
b6: (62, 130)
c6: (63, 131)
d6: (6, 74)
e6: (37, 105)
f6: (19, 87)
g6: (50, 118)
h6: (2, 68)(3, 67)(4, 66)(5, 65)(6, 64)(7, 63)(8, 62)(9, 61)(10, 60)(11, 59)(12, 58)(13, 57)(14, 56)(15, 55)(16, 54)(17, 53)(18, 52)(19, 51)(20, 50)(21, 49)(22, 48)(23, 47)(24, 46)(25, 45)(26, 44)(27, 43)(28, 42)(29, 41)(30, 40)(31, 39)(32, 38)(33, 37)(34, 36)(70, 136)(71, 135)(72, 134)(73, 133)(74, 132)(75, 131)(76, 130)(77, 129)(78, 128)(79, 127)(80, 126)(81, 125)(82, 124)(83, 123)(84, 122)(85, 121)(86, 120)(87, 119)(88, 118)(89, 117)(90, 116)(91, 115)(92, 114)(93, 113)(94, 112)(95, 111)(96, 110)(97, 109)(98, 108)(99, 107)(100, 106)(101, 105)(102, 104)

(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.

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&Graph
C4[ 136, 1 ]
136
-1 2 68 70 136
-2 1 3 69 71
-3 2 4 70 72
-4 3 5 71 73
-5 4 6 72 74
-6 5 7 73 75
-7 6 8 74 76
-8 77 7 9 75
-9 78 8 10 76
-10 11 77 79 9
-11 12 78 80 10
-12 11 13 79 81
-13 12 14 80 82
-14 13 15 81 83
-15 14 16 82 84
-16 15 17 83 85
-17 16 18 84 86
-18 17 19 85 87
-19 88 18 20 86
-20 89 19 21 87
-21 22 88 90 20
-22 23 89 91 21
-23 22 24 90 92
-24 23 25 91 93
-25 24 26 92 94
-26 25 27 93 95
-27 26 28 94 96
-28 27 29 95 97
-29 28 30 96 98
-30 99 29 31 97
-31 100 30 32 98
-32 33 99 101 31
-33 34 100 102 32
-34 33 35 101 103
-35 34 36 102 104
-36 35 37 103 105
-37 36 38 104 106
-38 37 39 105 107
-39 38 40 106 108
-40 39 41 107 109
-41 110 40 42 108
-42 111 41 43 109
-43 44 110 112 42
-44 45 111 113 43
-45 44 46 112 114
-46 45 47 113 115
-47 46 48 114 116
-48 47 49 115 117
-49 48 50 116 118
-50 49 51 117 119
-51 50 52 118 120
-52 121 51 53 119
-53 122 52 54 120
-54 55 121 123 53
-55 56 122 124 54
-56 55 57 123 125
-57 56 58 124 126
-58 57 59 125 127
-59 58 60 126 128
-60 59 61 127 129
-61 60 62 128 130
-62 61 63 129 131
-63 132 62 64 130
-64 133 63 65 131
-65 66 132 134 64
-66 67 133 135 65
-67 66 68 134 136
-68 1 67 69 135
-69 2 68 70 136
-70 1 3 69 71
-71 2 4 70 72
-72 3 5 71 73
-73 4 6 72 74
-74 5 7 73 75
-75 6 8 74 76
-76 77 7 9 75
-77 78 8 10 76
-78 11 77 79 9
-79 12 78 80 10
-80 11 13 79 81
-81 12 14 80 82
-82 13 15 81 83
-83 14 16 82 84
-84 15 17 83 85
-85 16 18 84 86
-86 17 19 85 87
-87 88 18 20 86
-88 89 19 21 87
-89 22 88 90 20
-90 23 89 91 21
-91 22 24 90 92
-92 23 25 91 93
-93 24 26 92 94
-94 25 27 93 95
-95 26 28 94 96
-96 27 29 95 97
-97 28 30 96 98
-98 99 29 31 97
-99 100 30 32 98
-100 33 99 101 31
-101 34 100 102 32
-102 33 35 101 103
-103 34 36 102 104
-104 35 37 103 105
-105 36 38 104 106
-106 37 39 105 107
-107 38 40 106 108
-108 39 41 107 109
-109 110 40 42 108
-110 111 41 43 109
-111 44 110 112 42
-112 45 111 113 43
-113 44 46 112 114
-114 45 47 113 115
-115 46 48 114 116
-116 47 49 115 117
-117 48 50 116 118
-118 49 51 117 119
-119 50 52 118 120
-120 121 51 53 119
-121 122 52 54 120
-122 55 121 123 53
-123 56 122 124 54
-124 55 57 123 125
-125 56 58 124 126
-126 57 59 125 127
-127 58 60 126 128
-128 59 61 127 129
-129 60 62 128 130
-130 61 63 129 131
-131 132 62 64 130
-132 133 63 65 131
-133 66 132 134 64
-134 67 133 135 65
-135 66 68 134 136
-136 1 67 69 135
0

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