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On this page are computer-accessible forms for the graph C4[ 138, 1 ] = W(69,2).

(I) Following is a form readable by MAGMA:

g:=Graph<138|{ {2, 3}, {136, 137}, {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}, {137, 138}, {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}, {1, 69}, {35, 103}, {34, 102}, {33, 101}, {32, 100}, {27, 95}, {26, 94}, {25, 93}, {24, 92}, {2, 70}, {3, 71}, {8, 76}, {9, 77}, {10, 78}, {11, 79}, {16, 84}, {17, 85}, {18, 86}, {19, 87}, {40, 108}, {41, 109}, {42, 110}, {43, 111}, {48, 116}, {49, 117}, {50, 118}, {51, 119}, {56, 124}, {57, 125}, {58, 126}, {59, 127}, {1, 71}, {33, 103}, {32, 102}, {25, 95}, {24, 94}, {8, 78}, {9, 79}, {16, 86}, {17, 87}, {40, 110}, {41, 111}, {48, 118}, {49, 119}, {56, 126}, {57, 127}, {2, 72}, {38, 108}, {35, 105}, {34, 104}, {23, 93}, {3, 73}, {6, 76}, {7, 77}, {18, 88}, {19, 89}, {22, 92}, {39, 109}, {50, 120}, {51, 121}, {54, 124}, {55, 125}, {4, 72}, {38, 106}, {37, 105}, {36, 104}, {5, 73}, {6, 74}, {7, 75}, {20, 88}, {21, 89}, {22, 90}, {23, 91}, {39, 107}, {52, 120}, {53, 121}, {54, 122}, {55, 123}, {4, 74}, {37, 107}, {36, 106}, {5, 75}, {20, 90}, {21, 91}, {52, 122}, {53, 123}, {10, 80}, {11, 81}, {14, 84}, {15, 85}, {42, 112}, {43, 113}, {46, 116}, {47, 117}, {12, 80}, {13, 81}, {14, 82}, {15, 83}, {44, 112}, {45, 113}, {46, 114}, {47, 115}, {12, 82}, {13, 83}, {44, 114}, {45, 115}, {26, 96}, {31, 101}, {30, 100}, {27, 97}, {28, 96}, {31, 99}, {30, 98}, {29, 97}, {28, 98}, {29, 99}, {63, 64}, {1, 138}, {58, 128}, {59, 129}, {62, 132}, {63, 133}, {60, 128}, {61, 129}, {62, 130}, {63, 131}, {60, 130}, {61, 131}, {64, 132}, {67, 135}, {65, 133}, {66, 134}, {64, 134}, {65, 135}, {66, 136}, {67, 137}, {68, 136}, {70, 138}, {69, 137}, {68, 138}, {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: (25, 94)
b: (48, 117)
c: (21, 90)
d: (45, 114)
e: (6, 75)
f: (59, 128)
g: (68, 137)
h: (5, 74)
m: (15, 84)
n1: (43, 112)
a1: (55, 124)
b1: (53, 122)
c1: (49, 118)
d1: (32, 101)
e1: (51, 120)
f1: (66, 135)
g1: (44, 113)
h1: (23, 92)
m1: (7, 76)
n2: (19, 88)
a2: (62, 131)
b2: (4, 73)
c2: (9, 78)
d2: (29, 98)
e2: (18, 87)
f2: (50, 119)
g2: (11, 80)
h2: (28, 97)
m2: (60, 129)
n3: (39, 108)
a3: (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, 137, 138)
b3: (14, 83)
c3: (20, 89)
d3: (41, 110)
e3: (47, 116)
f3: (12, 81)
g3: (33, 102)
h3: (3, 72)
m3: (56, 125)
n4: (27, 96)
a4: (69, 138)
b4: (54, 123)
c4: (42, 111)
d4: (57, 126)
e4: (35, 104)
f4: (13, 82)
g4: (36, 105)
h4: (46, 115)
m4: (8, 77)
n5: (52, 121)
a5: (17, 86)
b5: (38, 107)
c5: (61, 130)
d5: (30, 99)
e5: (63, 132)
f5: (65, 134)
g5: (58, 127)
h5: (22, 91)
m5: (24, 93)
n6: (40, 109)
a6: (2, 69)(3, 68)(4, 67)(5, 66)(6, 65)(7, 64)(8, 63)(9, 62)(10, 61)(11, 60)(12, 59)(13, 58)(14, 57)(15, 56)(16, 55)(17, 54)(18, 53)(19, 52)(20, 51)(21, 50)(22, 49)(23, 48)(24, 47)(25, 46)(26, 45)(27, 44)(28, 43)(29, 42)(30, 41)(31, 40)(32, 39)(33, 38)(34, 37)(35, 36)(71, 138)(72, 137)(73, 136)(74, 135)(75, 134)(76, 133)(77, 132)(78, 131)(79, 130)(80, 129)(81, 128)(82, 127)(83, 126)(84, 125)(85, 124)(86, 123)(87, 122)(88, 121)(89, 120)(90, 119)(91, 118)(92, 117)(93, 116)(94, 115)(95, 114)(96, 113)(97, 112)(98, 111)(99, 110)(100, 109)(101, 108)(102, 107)(103, 106)(104, 105)
b6: (10, 79)
c6: (31, 100)
d6: (16, 85)
e6: (26, 95)
f6: (67, 136)
g6: (64, 133)
h6: (2, 71)
m6: (37, 106)

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

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