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On this page are computer-accessible forms for the graph C4[ 54, 4 ] = DG(F18).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {48, 49} under the group generated by the following permutations:

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

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

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