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On this page are computer-accessible forms for the graph C4[ 52, 1 ] = W(26,2).

(I) Following is a form readable by MAGMA:

g:=Graph<52|{ {2, 3}, {50, 51}, {48, 49}, {46, 47}, {44, 45}, {42, 43}, {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}, {38, 39}, {40, 41}, {1, 2}, {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}, {23, 24}, {39, 40}, {2, 27}, {4, 29}, {6, 31}, {1, 26}, {4, 31}, {5, 30}, {1, 28}, {3, 30}, {2, 29}, {47, 48}, {15, 16}, {3, 28}, {5, 32}, {15, 42}, {7, 34}, {13, 40}, {21, 48}, {23, 50}, {6, 33}, {15, 40}, {14, 41}, {7, 32}, {22, 49}, {23, 48}, {8, 33}, {14, 39}, {10, 35}, {12, 37}, {24, 49}, {26, 51}, {8, 35}, {9, 34}, {12, 39}, {13, 38}, {24, 51}, {25, 50}, {9, 36}, {11, 38}, {25, 52}, {10, 37}, {11, 36}, {27, 52}, {1, 52}, {16, 41}, {20, 45}, {18, 43}, {22, 47}, {16, 43}, {20, 47}, {17, 42}, {21, 46}, {17, 44}, {19, 46}, {18, 45}, {19, 44}, {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: (21, 47)
b: (5, 31)
c: (8, 34)
d: (25, 51)
e: (9, 35)
f: (17, 43)
g: (14, 40)
h: (18, 44)
m: (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)
n1: (13, 39)
a1: (20, 46)
b1: (11, 37)
c1: (22, 48)
d1: (7, 33)
e1: (6, 32)
f1: (15, 41)
g1: (26, 52)
h1: (23, 49)
m1: (19, 45)
n2: (3, 29)
a2: (16, 42)
b2: (2, 28)
c2: (24, 50)
d2: (10, 36)
e2: (4, 30)
f2: (2, 26)(3, 25)(4, 24)(5, 23)(6, 22)(7, 21)(8, 20)(9, 19)(10, 18)(11, 17)(12, 16)(13, 15)(28, 52)(29, 51)(30, 50)(31, 49)(32, 48)(33, 47)(34, 46)(35, 45)(36, 44)(37, 43)(38, 42)(39, 41)

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

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