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

On this page are computer-accessible forms for the graph C4[ 53, 1 ] = C_53(1,23).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {2, 3} under the group generated by the following permutations:

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

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

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