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On this page are computer-accessible forms for the graph C4[ 54, 6 ] = PL(ProjLR(3,3)).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {10, 11} under the group generated by the following permutations:

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

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

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