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On this page are computer-accessible forms for the graph C4[ 68, 5 ] = SDD(C_17(1,4)).

(I) Following is a form readable by MAGMA:

g:=Graph<68|{ {32, 48}, {34, 50}, {33, 49}, {32, 49}, {34, 51}, {33, 50}, {3, 35}, {9, 41}, {5, 37}, {2, 35}, {5, 36}, {1, 35}, {29, 63}, {6, 36}, {7, 36}, {28, 63}, {15, 43}, {26, 62}, {25, 61}, {1, 36}, {27, 62}, {26, 63}, {24, 61}, {2, 39}, {12, 42}, {24, 62}, {14, 40}, {4, 35}, {15, 39}, {17, 57}, {18, 58}, {20, 60}, {14, 39}, {25, 48}, {16, 57}, {18, 59}, {19, 58}, {12, 38}, {27, 49}, {16, 58}, {21, 63}, {22, 60}, {13, 38}, {23, 60}, {22, 61}, {9, 37}, {31, 51}, {11, 39}, {17, 61}, {8, 37}, {11, 38}, {19, 62}, {6, 40}, {30, 48}, {8, 38}, {21, 59}, {10, 37}, {29, 50}, {20, 59}, {4, 52}, {31, 47}, {5, 53}, {30, 47}, {7, 53}, {28, 46}, {3, 48}, {29, 46}, {28, 47}, {15, 60}, {11, 56}, {9, 58}, {6, 53}, {5, 54}, {1, 53}, {26, 46}, {24, 44}, {1, 52}, {25, 44}, {24, 45}, {2, 52}, {27, 45}, {14, 56}, {7, 49}, {3, 52}, {26, 45}, {15, 56}, {14, 57}, {12, 59}, {4, 51}, {10, 50}, {16, 40}, {18, 42}, {23, 47}, {16, 41}, {17, 40}, {2, 56}, {13, 55}, {19, 41}, {22, 44}, {12, 55}, {18, 41}, {21, 46}, {10, 54}, {11, 55}, {23, 43}, {17, 44}, {22, 43}, {8, 54}, {13, 51}, {19, 45}, {20, 42}, {6, 57}, {9, 54}, {8, 55}, {20, 43}, {21, 42}, {4, 68}, {3, 65}, {7, 66}, {10, 67}, {13, 68}, {23, 64}, {25, 65}, {27, 66}, {31, 68}, {28, 64}, {29, 67}, {30, 64}, {30, 65}, {31, 64}, {32, 65}, {34, 67}, {32, 66}, {33, 67}, {33, 66}, {34, 68} }>;

(II) A more general form is to represent the graph as the orbit of {32, 48} under the group generated by the following permutations:

a: (45, 62)
b: (35, 52)
c: (37, 54)
d: (49, 66)
e: (38, 55)
f: (50, 67)
g: (44, 61)
h: (39, 56)
m: (2, 7)(3, 6)(4, 5)(8, 34)(9, 31)(10, 13)(11, 33)(12, 29)(14, 32)(15, 27)(16, 30)(17, 25)(18, 28)(19, 23)(20, 26)(22, 24)(35, 36)(37, 51)(38, 50)(39, 49)(40, 48)(41, 47)(42, 46)(43, 45)(52, 53)(54, 68)(55, 67)(56, 66)(57, 65)(58, 64)(59, 63)(60, 62)
n1: (51, 68)
a1: (47, 64)
b1: (36, 53)
c1: (41, 58)
d1: (42, 59)
e1: (1, 2, 14, 6)(3, 11, 17, 5)(4, 15, 16, 7)(8, 25)(9, 32, 13, 22)(10, 30, 12, 24)(18, 27, 34, 23)(19, 33, 31, 20)(21, 26, 29, 28)(35, 39, 40, 36)(37, 48, 38, 44)(41, 49, 51, 43)(42, 45, 50, 47)(52, 56, 57, 53)(54, 65, 55, 61)(58, 66, 68, 60)(59, 62, 67, 64)
f1: (46, 63)
g1: (40, 57)
h1: (48, 65)

(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[ 68, 5 ]
68
-1 35 36 52 53
-2 56 35 39 52
-3 35 48 52 65
-4 35 68 51 52
-5 36 37 53 54
-6 57 36 40 53
-7 66 36 49 53
-8 55 37 38 54
-9 58 37 41 54
-10 67 37 50 54
-11 55 56 38 39
-12 55 59 38 42
-13 55 68 38 51
-14 56 57 39 40
-15 56 60 39 43
-16 57 58 40 41
-17 44 57 61 40
-18 58 59 41 42
-19 45 58 62 41
-20 59 60 42 43
-21 46 59 63 42
-22 44 60 61 43
-23 47 60 64 43
-24 44 45 61 62
-25 44 48 61 65
-26 45 46 62 63
-27 66 45 49 62
-28 46 47 63 64
-29 67 46 50 63
-30 47 48 64 65
-31 68 47 51 64
-32 66 48 49 65
-33 66 67 49 50
-34 67 68 50 51
-35 1 2 3 4
-36 1 5 6 7
-37 5 8 9 10
-38 11 12 13 8
-39 11 2 14 15
-40 14 16 6 17
-41 16 18 19 9
-42 12 18 20 21
-43 22 23 15 20
-44 22 24 25 17
-45 24 26 27 19
-46 26 28 29 21
-47 23 28 30 31
-48 3 25 30 32
-49 33 27 7 32
-50 33 34 29 10
-51 34 13 4 31
-52 1 2 3 4
-53 1 5 6 7
-54 5 8 9 10
-55 11 12 13 8
-56 11 2 14 15
-57 14 16 6 17
-58 16 18 19 9
-59 12 18 20 21
-60 22 23 15 20
-61 22 24 25 17
-62 24 26 27 19
-63 26 28 29 21
-64 23 28 30 31
-65 3 25 30 32
-66 33 27 7 32
-67 33 34 29 10
-68 34 13 4 31
0

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