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On this page are computer-accessible forms for the graph C4[ 56, 7 ] = SDD(BC_7(0,1,2,4)).

(I) Following is a form readable by MAGMA:

g:=Graph<56|{ {12, 31}, {11, 31}, {10, 31}, {8, 30}, {9, 31}, {6, 30}, {4, 29}, {7, 30}, {5, 30}, {1, 29}, {3, 29}, {2, 29}, {5, 37}, {24, 56}, {23, 55}, {14, 46}, {7, 39}, {6, 38}, {8, 41}, {15, 46}, {12, 45}, {17, 51}, {22, 52}, {11, 40}, {13, 46}, {8, 44}, {28, 56}, {9, 45}, {18, 54}, {19, 55}, {1, 36}, {3, 38}, {21, 48}, {11, 45}, {22, 48}, {12, 42}, {2, 37}, {23, 48}, {21, 50}, {15, 40}, {10, 45}, {16, 55}, {3, 43}, {25, 49}, {24, 48}, {2, 43}, {26, 51}, {14, 39}, {13, 36}, {5, 44}, {1, 43}, {27, 49}, {6, 44}, {7, 44}, {26, 49}, {25, 50}, {4, 40}, {20, 56}, {10, 39}, {28, 49}, {13, 32}, {14, 32}, {27, 53}, {4, 43}, {15, 32}, {9, 38}, {16, 32}, {22, 38}, {17, 33}, {2, 51}, {21, 36}, {4, 54}, {24, 42}, {7, 53}, {6, 52}, {19, 33}, {1, 50}, {18, 33}, {12, 56}, {22, 34}, {17, 37}, {20, 33}, {23, 34}, {5, 51}, {28, 42}, {3, 52}, {21, 34}, {27, 35}, {15, 54}, {26, 35}, {16, 41}, {18, 40}, {25, 35}, {24, 34}, {19, 41}, {14, 53}, {20, 47}, {19, 47}, {27, 39}, {9, 52}, {25, 36}, {11, 54}, {18, 47}, {16, 46}, {23, 41}, {17, 47}, {20, 42}, {8, 55}, {28, 35}, {26, 37}, {13, 50}, {10, 53} }>;

(II) A more general form is to represent the graph as the orbit of {12, 31} under the group generated by the following permutations:

a: (29, 43)
b: (38, 52)
c: (2, 21, 4, 25, 3, 13)(5, 23, 18, 28, 9, 14)(6, 16, 17, 24, 11, 27)(7, 8, 19, 20, 12, 10)(15, 26, 22)(29, 36)(30, 41, 33, 42, 31, 39)(32, 37, 34, 40, 35, 38)(43, 50)(44, 55, 47, 56, 45, 53)(46, 51, 48, 54, 49, 52)
d: (42, 56)
e: (39, 53)
f: (36, 50)
g: (30, 44)
h: (2, 4, 3)(5, 18, 9)(6, 17, 11)(7, 19, 12)(8, 20, 10)(13, 21, 25)(14, 23, 28)(15, 22, 26)(16, 24, 27)(30, 33, 31)(32, 34, 35)(37, 40, 38)(39, 41, 42)(44, 47, 45)(46, 48, 49)(51, 54, 52)(53, 55, 56)
m: (34, 48)
n1: (40, 54)
a1: (1, 2)(3, 4)(5, 13)(6, 15)(7, 14)(8, 16)(9, 11)(17, 21)(18, 22)(19, 23)(20, 24)(25, 26)(30, 32)(33, 34)(36, 37)(38, 40)(44, 46)(47, 48)(50, 51)(52, 54)
b1: (33, 47)
c1: (35, 49)
d1: (41, 55)
e1: (37, 51)
f1: (2, 3)(5, 6)(7, 8)(9, 17)(10, 19)(11, 18)(12, 20)(14, 16)(21, 25)(22, 26)(23, 27)(24, 28)(31, 33)(34, 35)(37, 38)(39, 41)(45, 47)(48, 49)(51, 52)(53, 55)

(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[ 56, 7 ]
56
-1 36 50 29 43
-2 37 29 51 43
-3 38 29 52 43
-4 29 40 43 54
-5 44 37 51 30
-6 44 38 30 52
-7 44 39 30 53
-8 44 55 30 41
-9 45 38 52 31
-10 45 39 31 53
-11 45 40 31 54
-12 45 56 31 42
-13 46 36 50 32
-14 46 39 53 32
-15 46 40 32 54
-16 55 46 41 32
-17 33 47 37 51
-18 33 47 40 54
-19 33 55 47 41
-20 33 56 47 42
-21 34 36 48 50
-22 34 48 38 52
-23 55 34 48 41
-24 34 56 48 42
-25 35 36 49 50
-26 35 37 49 51
-27 35 49 39 53
-28 56 35 49 42
-29 1 2 3 4
-30 5 6 7 8
-31 11 12 9 10
-32 13 14 15 16
-33 17 18 19 20
-34 22 23 24 21
-35 25 26 27 28
-36 1 13 25 21
-37 2 26 5 17
-38 22 3 6 9
-39 14 27 7 10
-40 11 4 15 18
-41 23 16 8 19
-42 12 24 28 20
-43 1 2 3 4
-44 5 6 7 8
-45 11 12 9 10
-46 13 14 15 16
-47 17 18 19 20
-48 22 23 24 21
-49 25 26 27 28
-50 1 13 25 21
-51 2 26 5 17
-52 22 3 6 9
-53 14 27 7 10
-54 11 4 15 18
-55 23 16 8 19
-56 12 24 28 20
0

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