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On this page are computer-accessible forms for the graph C4[ 126, 1 ] = W(63,2).

(I) Following is a form readable by MAGMA:

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

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

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

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