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On this page are computer-accessible forms for the graph C4[ 128, 1 ] = W(64,2).

(I) Following is a form readable by MAGMA:

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

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

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