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On this page are computer-accessible forms for the graph C4[ 60, 3 ] = C_60(1,19).

(I) Following is a form readable by MAGMA:

g:=Graph<60|{ {2, 3}, {58, 59}, {56, 57}, {54, 55}, {52, 53}, {50, 51}, {48, 49}, {46, 47}, {44, 45}, {42, 43}, {40, 41}, {38, 39}, {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}, {1, 2}, {57, 58}, {53, 54}, {49, 50}, {45, 46}, {41, 42}, {21, 22}, {17, 18}, {5, 6}, {9, 10}, {13, 14}, {25, 26}, {29, 30}, {33, 34}, {37, 38}, {3, 4}, {59, 60}, {51, 52}, {43, 44}, {19, 20}, {11, 12}, {27, 28}, {35, 36}, {7, 8}, {55, 56}, {39, 40}, {23, 24}, {4, 23}, {40, 59}, {8, 27}, {12, 31}, {32, 51}, {36, 55}, {1, 20}, {41, 60}, {3, 22}, {9, 28}, {11, 30}, {33, 52}, {35, 54}, {2, 21}, {10, 29}, {34, 53}, {5, 24}, {39, 58}, {7, 26}, {37, 56}, {6, 25}, {47, 48}, {38, 57}, {15, 16}, {2, 43}, {18, 59}, {16, 57}, {4, 45}, {6, 47}, {1, 42}, {17, 58}, {5, 46}, {13, 32}, {15, 34}, {29, 48}, {31, 50}, {3, 44}, {19, 60}, {14, 33}, {30, 49}, {16, 35}, {20, 39}, {24, 43}, {28, 47}, {17, 36}, {19, 38}, {25, 44}, {27, 46}, {7, 48}, {18, 37}, {15, 56}, {26, 45}, {8, 49}, {10, 51}, {12, 53}, {14, 55}, {9, 50}, {13, 54}, {1, 60}, {21, 40}, {23, 42}, {11, 52}, {22, 41}, {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: (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, 55, 56, 57, 58, 59, 60)
b: (2, 42)(3, 23)(5, 45)(6, 26)(8, 48)(9, 29)(11, 51)(12, 32)(14, 54)(15, 35)(17, 57)(18, 38)(20, 60)(21, 41)(24, 44)(27, 47)(30, 50)(33, 53)(36, 56)(39, 59)
c: (2, 20)(3, 39)(4, 58)(5, 17)(6, 36)(7, 55)(8, 14)(9, 33)(10, 52)(12, 30)(13, 49)(15, 27)(16, 46)(18, 24)(19, 43)(22, 40)(23, 59)(25, 37)(26, 56)(28, 34)(29, 53)(32, 50)(35, 47)(38, 44)(42, 60)(45, 57)(48, 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.

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&Graph
C4[ 60, 3 ]
60
-1 2 60 20 42
-2 1 3 21 43
-3 22 44 2 4
-4 23 45 3 5
-5 24 46 4 6
-6 25 47 5 7
-7 26 48 6 8
-8 27 49 7 9
-9 28 50 8 10
-10 11 29 51 9
-11 12 30 52 10
-12 11 13 31 53
-13 12 14 32 54
-14 33 55 13 15
-15 34 56 14 16
-16 35 57 15 17
-17 36 58 16 18
-18 37 59 17 19
-19 38 60 18 20
-20 1 39 19 21
-21 22 2 40 20
-22 23 3 41 21
-23 22 24 4 42
-24 23 25 5 43
-25 44 24 26 6
-26 45 25 27 7
-27 46 26 28 8
-28 47 27 29 9
-29 48 28 30 10
-30 11 49 29 31
-31 12 50 30 32
-32 33 13 51 31
-33 34 14 52 32
-34 33 35 15 53
-35 34 36 16 54
-36 55 35 37 17
-37 56 36 38 18
-38 57 37 39 19
-39 58 38 40 20
-40 59 39 41 21
-41 22 60 40 42
-42 1 23 41 43
-43 44 2 24 42
-44 45 3 25 43
-45 44 46 4 26
-46 45 47 5 27
-47 46 48 6 28
-48 47 49 7 29
-49 48 50 8 30
-50 49 51 9 31
-51 50 52 10 32
-52 11 33 51 53
-53 12 34 52 54
-54 55 13 35 53
-55 56 14 36 54
-56 55 57 15 37
-57 56 58 16 38
-58 57 59 17 39
-59 58 60 18 40
-60 1 59 19 41
0

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