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On this page are computer-accessible forms for the graph C4[ 54, 2 ] = DW(18,3).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {18, 19} under the group generated by the following permutations:

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

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

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