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On this page are computer-accessible forms for the graph C4[ 52, 4 ] = SDD(C_13(1,5)).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {16, 31} under the group generated by the following permutations:

a: (2, 7)(3, 6)(4, 5)(8, 26)(9, 22)(10, 16)(11, 25)(12, 20)(14, 24)(15, 18)(17, 23)(19, 21)(27, 28)(29, 39)(30, 38)(31, 37)(32, 36)(33, 35)(40, 41)(42, 52)(43, 51)(44, 50)(45, 49)(46, 48)
b: (27, 40)
c: (1, 2, 17, 6)(3, 14, 20, 5)(4, 18, 19, 7)(8, 12, 11, 13)(9, 23, 16, 25)(10, 21, 15, 26)(22, 24)(27, 32, 33, 28)(29, 35, 31, 38)(34, 36, 39, 37)(40, 45, 46, 41)(42, 48, 44, 51)(47, 49, 52, 50)
d: (36, 49)
e: (37, 50)
f: (30, 43)
g: (33, 46)
h: (34, 47)
m: (39, 52)
n1: (28, 41)
a1: (38, 51)
b1: (32, 45)
c1: (35, 48)
d1: (31, 44)

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

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