[Home] [Table] [Glossary] [Families]

On this page are computer-accessible forms for the graph C4[ 54, 3 ] = PS(6,9;2).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {36, 37} under the group generated by the following permutations:

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

**************

&Graph
C4[ 54, 3 ]
54
-1 11 50 18 51
-2 12 51 52 10
-3 11 13 52 53
-4 12 14 53 54
-5 13 46 15 54
-6 46 14 47 16
-7 47 15 48 17
-8 48 16 49 18
-9 49 17 50 10
-10 2 26 9 21
-11 22 1 3 27
-12 23 2 4 19
-13 24 3 5 20
-14 25 4 6 21
-15 22 26 5 7
-16 23 27 6 8
-17 24 7 19 9
-18 1 25 8 20
-19 33 12 17 32
-20 33 34 13 18
-21 34 35 14 10
-22 11 35 36 15
-23 12 36 16 28
-24 13 17 28 29
-25 14 18 29 30
-26 15 30 31 10
-27 11 16 31 32
-28 23 45 24 38
-29 24 25 37 39
-30 25 26 38 40
-31 26 27 39 41
-32 27 40 19 42
-33 19 41 20 43
-34 44 20 42 21
-35 22 45 21 43
-36 22 44 23 37
-37 36 48 29 53
-38 49 28 30 54
-39 46 50 29 31
-40 47 51 30 32
-41 33 48 52 31
-42 34 49 53 32
-43 33 35 50 54
-44 34 46 36 51
-45 35 47 28 52
-46 44 5 6 39
-47 45 6 7 40
-48 37 7 8 41
-49 38 8 9 42
-50 1 39 9 43
-51 44 1 2 40
-52 45 2 3 41
-53 3 4 37 42
-54 4 5 38 43
0

**************