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On this page are computer-accessible forms for the graph C4[ 82, 2 ] = C_82(1,9).

(I) Following is a form readable by MAGMA:

g:=Graph<82|{ {2, 3}, {80, 81}, {78, 79}, {76, 77}, {74, 75}, {42, 43}, {40, 41}, {38, 39}, {36, 37}, {34, 35}, {32, 33}, {30, 31}, {28, 29}, {4, 5}, {6, 7}, {8, 9}, {10, 11}, {12, 13}, {14, 15}, {16, 17}, {18, 19}, {20, 21}, {22, 23}, {24, 25}, {26, 27}, {44, 45}, {46, 47}, {48, 49}, {50, 51}, {52, 53}, {54, 55}, {56, 57}, {58, 59}, {60, 61}, {62, 63}, {64, 65}, {66, 67}, {68, 69}, {70, 71}, {72, 73}, {1, 2}, {81, 82}, {77, 78}, {41, 42}, {37, 38}, {33, 34}, {29, 30}, {5, 6}, {9, 10}, {13, 14}, {17, 18}, {21, 22}, {25, 26}, {45, 46}, {49, 50}, {53, 54}, {57, 58}, {61, 62}, {65, 66}, {69, 70}, {73, 74}, {3, 4}, {75, 76}, {43, 44}, {35, 36}, {27, 28}, {11, 12}, {19, 20}, {51, 52}, {59, 60}, {67, 68}, {2, 11}, {38, 47}, {36, 45}, {34, 43}, {32, 41}, {4, 13}, {6, 15}, {16, 25}, {18, 27}, {20, 29}, {22, 31}, {48, 57}, {50, 59}, {52, 61}, {54, 63}, {64, 73}, {66, 75}, {68, 77}, {70, 79}, {1, 10}, {37, 46}, {33, 42}, {5, 14}, {17, 26}, {21, 30}, {49, 58}, {53, 62}, {65, 74}, {69, 78}, {3, 12}, {39, 40}, {35, 44}, {7, 8}, {19, 28}, {23, 24}, {51, 60}, {55, 56}, {67, 76}, {71, 72}, {7, 16}, {39, 48}, {15, 24}, {47, 56}, {71, 80}, {8, 17}, {42, 51}, {40, 49}, {10, 19}, {12, 21}, {14, 23}, {44, 53}, {46, 55}, {72, 81}, {9, 18}, {73, 82}, {41, 50}, {13, 22}, {45, 54}, {11, 20}, {79, 80}, {15, 16}, {43, 52}, {47, 48}, {23, 32}, {31, 40}, {24, 33}, {30, 39}, {28, 37}, {26, 35}, {25, 34}, {29, 38}, {27, 36}, {31, 32}, {2, 75}, {4, 77}, {6, 79}, {1, 74}, {5, 78}, {3, 76}, {1, 82}, {7, 80}, {8, 81}, {9, 82}, {55, 64}, {63, 72}, {56, 65}, {58, 67}, {60, 69}, {62, 71}, {57, 66}, {61, 70}, {59, 68}, {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, 74, 82, 10)(3, 65, 81, 19)(4, 56, 80, 28)(5, 47, 79, 37)(6, 38, 78, 46)(7, 29, 77, 55)(8, 20, 76, 64)(9, 11, 75, 73)(12, 66, 72, 18)(13, 57, 71, 27)(14, 48, 70, 36)(15, 39, 69, 45)(16, 30, 68, 54)(17, 21, 67, 63)(22, 58, 62, 26)(23, 49, 61, 35)(24, 40, 60, 44)(25, 31, 59, 53)(32, 50, 52, 34)(33, 41, 51, 43)
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, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82)

(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[ 82, 2 ]
82
-1 2 82 74 10
-2 11 1 3 75
-3 12 2 4 76
-4 77 13 3 5
-5 78 14 4 6
-6 79 15 5 7
-7 80 16 6 8
-8 81 17 7 9
-9 82 18 8 10
-10 11 1 19 9
-11 12 2 20 10
-12 11 13 3 21
-13 22 12 14 4
-14 23 13 15 5
-15 24 14 16 6
-16 25 15 17 7
-17 26 16 18 8
-18 27 17 19 9
-19 28 18 20 10
-20 11 29 19 21
-21 22 12 30 20
-22 23 13 31 21
-23 22 24 14 32
-24 33 23 25 15
-25 34 24 26 16
-26 35 25 27 17
-27 36 26 28 18
-28 37 27 29 19
-29 38 28 30 20
-30 39 29 31 21
-31 22 40 30 32
-32 33 23 41 31
-33 34 24 42 32
-34 33 35 25 43
-35 44 34 36 26
-36 45 35 37 27
-37 46 36 38 28
-38 47 37 39 29
-39 48 38 40 30
-40 49 39 41 31
-41 50 40 42 32
-42 33 51 41 43
-43 44 34 52 42
-44 45 35 53 43
-45 44 46 36 54
-46 55 45 47 37
-47 56 46 48 38
-48 57 47 49 39
-49 58 48 50 40
-50 59 49 51 41
-51 60 50 52 42
-52 61 51 53 43
-53 44 62 52 54
-54 55 45 63 53
-55 56 46 64 54
-56 55 57 47 65
-57 66 56 58 48
-58 67 57 59 49
-59 68 58 60 50
-60 69 59 61 51
-61 70 60 62 52
-62 71 61 63 53
-63 72 62 64 54
-64 55 73 63 65
-65 66 56 74 64
-66 67 57 75 65
-67 66 68 58 76
-68 77 67 69 59
-69 78 68 70 60
-70 79 69 71 61
-71 80 70 72 62
-72 81 71 73 63
-73 82 72 74 64
-74 1 73 75 65
-75 66 2 74 76
-76 77 67 3 75
-77 78 68 4 76
-78 77 79 69 5
-79 78 80 70 6
-80 79 81 71 7
-81 80 82 72 8
-82 1 81 73 9
0

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