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On this page are computer-accessible forms for the graph C4[ 106, 1 ] = W(53,2).

(I) Following is a form readable by MAGMA:

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

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

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