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On this page are computer-accessible forms for the graph C4[ 66, 2 ] = C_66(1,23).

(I) Following is a form readable by MAGMA:

g:=Graph<66|{ {2, 3}, {64, 65}, {62, 63}, {60, 61}, {58, 59}, {56, 57}, {26, 27}, {24, 25}, {22, 23}, {20, 21}, {18, 19}, {4, 5}, {6, 7}, {8, 9}, {10, 11}, {12, 13}, {14, 15}, {16, 17}, {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}, {1, 2}, {65, 66}, {61, 62}, {57, 58}, {25, 26}, {21, 22}, {17, 18}, {5, 6}, {9, 10}, {13, 14}, {29, 30}, {33, 34}, {37, 38}, {41, 42}, {45, 46}, {49, 50}, {53, 54}, {3, 4}, {59, 60}, {19, 20}, {11, 12}, {27, 28}, {35, 36}, {43, 44}, {51, 52}, {7, 8}, {55, 56}, {23, 24}, {39, 40}, {8, 31}, {32, 55}, {40, 63}, {1, 24}, {3, 26}, {5, 28}, {7, 30}, {33, 56}, {35, 58}, {37, 60}, {39, 62}, {2, 25}, {6, 29}, {34, 57}, {38, 61}, {4, 27}, {15, 16}, {36, 59}, {47, 48}, {9, 32}, {25, 48}, {11, 34}, {13, 36}, {15, 38}, {27, 50}, {29, 52}, {31, 54}, {4, 47}, {26, 49}, {20, 63}, {10, 33}, {14, 37}, {16, 59}, {30, 53}, {1, 44}, {19, 62}, {17, 60}, {3, 46}, {2, 45}, {18, 61}, {12, 35}, {28, 51}, {5, 48}, {7, 50}, {13, 56}, {15, 58}, {6, 49}, {24, 47}, {14, 57}, {16, 39}, {17, 40}, {23, 46}, {21, 44}, {19, 42}, {8, 51}, {22, 45}, {18, 41}, {12, 55}, {9, 52}, {11, 54}, {10, 53}, {20, 43}, {31, 32}, {1, 66}, {21, 64}, {23, 66}, {22, 65}, {41, 64}, {43, 66}, {42, 65}, {63, 64} }>;

(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)(3, 47)(5, 27)(6, 50)(8, 30)(9, 53)(11, 33)(12, 56)(14, 36)(15, 59)(17, 39)(18, 62)(20, 42)(21, 65)(23, 45)(26, 48)(29, 51)(32, 54)(35, 57)(38, 60)(41, 63)(44, 66)
b: (2, 44)(3, 21)(4, 64)(5, 41)(6, 18)(7, 61)(8, 38)(9, 15)(10, 58)(11, 35)(13, 55)(14, 32)(16, 52)(17, 29)(19, 49)(20, 26)(22, 46)(24, 66)(25, 43)(27, 63)(28, 40)(30, 60)(31, 37)(33, 57)(36, 54)(39, 51)(42, 48)(47, 65)(50, 62)(53, 59)
c: (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, 61, 62, 63, 64, 65, 66)

(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[ 66, 2 ]
66
-1 44 66 2 24
-2 1 45 3 25
-3 2 46 4 26
-4 3 47 5 27
-5 4 48 6 28
-6 5 49 7 29
-7 6 50 8 30
-8 7 51 9 31
-9 8 52 10 32
-10 11 33 9 53
-11 12 34 10 54
-12 11 55 13 35
-13 12 56 14 36
-14 13 57 15 37
-15 14 58 16 38
-16 15 59 17 39
-17 16 60 18 40
-18 17 61 19 41
-19 18 62 20 42
-20 19 63 21 43
-21 22 44 20 64
-22 23 45 21 65
-23 22 66 24 46
-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 8 30 32 54
-32 33 55 9 31
-33 34 56 10 32
-34 11 33 35 57
-35 12 34 36 58
-36 13 35 37 59
-37 14 36 38 60
-38 15 37 39 61
-39 16 38 40 62
-40 17 39 41 63
-41 18 40 42 64
-42 19 41 43 65
-43 44 66 20 42
-44 1 45 21 43
-45 22 44 2 46
-46 23 45 3 47
-47 24 46 4 48
-48 25 47 5 49
-49 26 48 6 50
-50 27 49 7 51
-51 28 50 8 52
-52 29 51 9 53
-53 30 52 10 54
-54 11 55 31 53
-55 12 56 32 54
-56 33 55 13 57
-57 34 56 14 58
-58 35 57 15 59
-59 36 58 16 60
-60 37 59 17 61
-61 38 60 18 62
-62 39 61 19 63
-63 40 62 20 64
-64 41 63 21 65
-65 22 66 42 64
-66 1 23 43 65
0

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