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On this page are computer-accessible forms for the graph C4[ 54, 1 ] = W(27,2).

(I) Following is a form readable by MAGMA:

g:=Graph<54|{ {2, 3}, {52, 53}, {50, 51}, {48, 49}, {46, 47}, {44, 45}, {42, 43}, {40, 41}, {38, 39}, {20, 21}, {18, 19}, {16, 17}, {14, 15}, {4, 5}, {6, 7}, {8, 9}, {10, 11}, {12, 13}, {22, 23}, {24, 25}, {26, 27}, {28, 29}, {30, 31}, {32, 33}, {34, 35}, {36, 37}, {1, 2}, {53, 54}, {49, 50}, {45, 46}, {41, 42}, {17, 18}, {5, 6}, {9, 10}, {13, 14}, {21, 22}, {25, 26}, {29, 30}, {33, 34}, {37, 38}, {3, 4}, {51, 52}, {43, 44}, {19, 20}, {11, 12}, {27, 28}, {35, 36}, {7, 8}, {39, 40}, {23, 24}, {1, 27}, {4, 30}, {5, 31}, {1, 29}, {2, 30}, {3, 31}, {2, 28}, {3, 29}, {15, 16}, {47, 48}, {4, 32}, {15, 43}, {14, 42}, {13, 41}, {5, 33}, {6, 34}, {7, 35}, {12, 40}, {20, 48}, {21, 49}, {22, 50}, {23, 51}, {6, 32}, {15, 41}, {14, 40}, {7, 33}, {22, 48}, {23, 49}, {8, 34}, {13, 39}, {9, 35}, {12, 38}, {24, 50}, {25, 51}, {28, 54}, {8, 36}, {9, 37}, {10, 38}, {11, 39}, {24, 52}, {25, 53}, {26, 54}, {10, 36}, {11, 37}, {26, 52}, {27, 53}, {1, 54}, {16, 42}, {17, 43}, {20, 46}, {21, 47}, {16, 44}, {19, 47}, {18, 46}, {17, 45}, {18, 44}, {19, 45}, {31, 32} }>;

(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: (24, 51)
b: (26, 53)
c: (4, 31)
d: (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)
e: (14, 41)
f: (9, 36)
g: (19, 46)
h: (2, 29)
m: (10, 37)
n1: (16, 43)
a1: (27, 54)
b1: (18, 45)
c1: (3, 30)
d1: (23, 50)
e1: (15, 42)
f1: (22, 49)
g1: (8, 35)
h1: (11, 38)
m1: (7, 34)
n2: (2, 27)(3, 26)(4, 25)(5, 24)(6, 23)(7, 22)(8, 21)(9, 20)(10, 19)(11, 18)(12, 17)(13, 16)(14, 15)(29, 54)(30, 53)(31, 52)(32, 51)(33, 50)(34, 49)(35, 48)(36, 47)(37, 46)(38, 45)(39, 44)(40, 43)(41, 42)
a2: (17, 44)
b2: (6, 33)
c2: (25, 52)
d2: (21, 48)
e2: (5, 32)
f2: (20, 47)
g2: (12, 39)

(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[ 54, 1 ]
54
-1 2 27 29 54
-2 1 3 28 30
-3 2 4 29 31
-4 3 5 30 32
-5 33 4 6 31
-6 34 5 7 32
-7 33 35 6 8
-8 34 36 7 9
-9 35 37 8 10
-10 11 36 38 9
-11 12 37 39 10
-12 11 13 38 40
-13 12 14 39 41
-14 13 15 40 42
-15 14 16 41 43
-16 44 15 17 42
-17 45 16 18 43
-18 44 46 17 19
-19 45 47 18 20
-20 46 48 19 21
-21 22 47 49 20
-22 23 48 50 21
-23 22 24 49 51
-24 23 25 50 52
-25 24 26 51 53
-26 25 27 52 54
-27 1 26 28 53
-28 2 27 29 54
-29 1 3 28 30
-30 2 4 29 31
-31 3 5 30 32
-32 33 4 6 31
-33 34 5 7 32
-34 33 35 6 8
-35 34 36 7 9
-36 35 37 8 10
-37 11 36 38 9
-38 12 37 39 10
-39 11 13 38 40
-40 12 14 39 41
-41 13 15 40 42
-42 14 16 41 43
-43 44 15 17 42
-44 45 16 18 43
-45 44 46 17 19
-46 45 47 18 20
-47 46 48 19 21
-48 22 47 49 20
-49 23 48 50 21
-50 22 24 49 51
-51 23 25 50 52
-52 24 26 51 53
-53 25 27 52 54
-54 1 26 28 53
0

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