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On this page are computer-accessible forms for the graph C4[ 109, 1 ] = C_109(1,33).

(I) Following is a form readable by MAGMA:

g:=Graph<109|{ {2, 3}, {108, 109}, {106, 107}, {104, 105}, {102, 103}, {100, 101}, {98, 99}, {96, 97}, {94, 95}, {92, 93}, {90, 91}, {88, 89}, {42, 43}, {40, 41}, {38, 39}, {36, 37}, {34, 35}, {32, 33}, {30, 31}, {28, 29}, {26, 27}, {24, 25}, {4, 5}, {6, 7}, {8, 9}, {10, 11}, {12, 13}, {14, 15}, {16, 17}, {18, 19}, {20, 21}, {22, 23}, {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, 83}, {84, 85}, {86, 87}, {1, 2}, {105, 106}, {101, 102}, {97, 98}, {93, 94}, {89, 90}, {41, 42}, {37, 38}, {33, 34}, {29, 30}, {25, 26}, {5, 6}, {9, 10}, {13, 14}, {17, 18}, {21, 22}, {45, 46}, {49, 50}, {53, 54}, {57, 58}, {61, 62}, {65, 66}, {69, 70}, {73, 74}, {77, 78}, {81, 82}, {85, 86}, {3, 4}, {107, 108}, {99, 100}, {91, 92}, {43, 44}, {35, 36}, {27, 28}, {11, 12}, {19, 20}, {51, 52}, {59, 60}, {67, 68}, {75, 76}, {83, 84}, {7, 8}, {103, 104}, {39, 40}, {23, 24}, {55, 56}, {71, 72}, {87, 88}, {15, 16}, {47, 48}, {79, 80}, {2, 35}, {30, 63}, {28, 61}, {26, 59}, {24, 57}, {4, 37}, {6, 39}, {8, 41}, {10, 43}, {12, 45}, {14, 47}, {16, 49}, {18, 51}, {20, 53}, {22, 55}, {64, 97}, {66, 99}, {68, 101}, {70, 103}, {72, 105}, {74, 107}, {76, 109}, {1, 34}, {29, 62}, {25, 58}, {5, 38}, {9, 42}, {13, 46}, {17, 50}, {21, 54}, {65, 98}, {69, 102}, {73, 106}, {3, 36}, {27, 60}, {11, 44}, {19, 52}, {67, 100}, {75, 108}, {7, 40}, {23, 56}, {71, 104}, {15, 48}, {95, 96}, {31, 32}, {1, 77}, {33, 109}, {32, 108}, {2, 78}, {3, 79}, {16, 92}, {17, 93}, {18, 94}, {19, 95}, {4, 80}, {5, 81}, {6, 82}, {7, 83}, {12, 88}, {13, 89}, {14, 90}, {15, 91}, {8, 84}, {9, 85}, {10, 86}, {11, 87}, {31, 64}, {63, 96}, {32, 65}, {42, 75}, {40, 73}, {38, 71}, {36, 69}, {34, 67}, {44, 77}, {46, 79}, {48, 81}, {50, 83}, {52, 85}, {54, 87}, {56, 89}, {58, 91}, {60, 93}, {62, 95}, {33, 66}, {41, 74}, {37, 70}, {45, 78}, {49, 82}, {53, 86}, {57, 90}, {61, 94}, {35, 68}, {43, 76}, {51, 84}, {59, 92}, {1, 109}, {39, 72}, {55, 88}, {20, 96}, {31, 107}, {30, 106}, {29, 105}, {28, 104}, {21, 97}, {22, 98}, {23, 99}, {24, 100}, {27, 103}, {26, 102}, {25, 101}, {47, 80}, {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, 34, 109, 77)(3, 67, 108, 44)(4, 100, 107, 11)(5, 24, 106, 87)(6, 57, 105, 54)(7, 90, 104, 21)(8, 14, 103, 97)(9, 47, 102, 64)(10, 80, 101, 31)(12, 37, 99, 74)(13, 70, 98, 41)(15, 27, 96, 84)(16, 60, 95, 51)(17, 93, 94, 18)(19, 50, 92, 61)(20, 83, 91, 28)(22, 40, 89, 71)(23, 73, 88, 38)(25, 30, 86, 81)(26, 63, 85, 48)(29, 53, 82, 58)(32, 43, 79, 68)(33, 76, 78, 35)(36, 66, 75, 45)(39, 56, 72, 55)(42, 46, 69, 65)(49, 59, 62, 52)
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, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109)

(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[ 109, 1 ]
109
-1 77 34 2 109
-2 1 78 35 3
-3 2 79 36 4
-4 3 80 37 5
-5 4 81 38 6
-6 5 82 39 7
-7 6 83 40 8
-8 7 84 41 9
-9 8 85 42 10
-10 11 9 86 43
-11 44 12 10 87
-12 11 88 45 13
-13 12 89 46 14
-14 13 90 47 15
-15 14 91 48 16
-16 15 92 49 17
-17 16 93 50 18
-18 17 94 51 19
-19 18 95 52 20
-20 19 96 53 21
-21 22 20 97 54
-22 55 23 21 98
-23 22 99 56 24
-24 23 100 57 25
-25 24 101 58 26
-26 25 102 59 27
-27 26 103 60 28
-28 27 104 61 29
-29 28 105 62 30
-30 29 106 63 31
-31 30 107 64 32
-32 33 31 108 65
-33 66 34 32 109
-34 33 1 67 35
-35 34 2 68 36
-36 35 3 69 37
-37 36 4 70 38
-38 37 5 71 39
-39 38 6 72 40
-40 39 7 73 41
-41 40 8 74 42
-42 41 9 75 43
-43 44 42 10 76
-44 11 77 45 43
-45 44 12 78 46
-46 45 13 79 47
-47 46 14 80 48
-48 47 15 81 49
-49 48 16 82 50
-50 49 17 83 51
-51 50 18 84 52
-52 51 19 85 53
-53 52 20 86 54
-54 55 53 21 87
-55 22 88 56 54
-56 55 23 89 57
-57 56 24 90 58
-58 57 25 91 59
-59 58 26 92 60
-60 59 27 93 61
-61 60 28 94 62
-62 61 29 95 63
-63 62 30 96 64
-64 63 31 97 65
-65 66 64 32 98
-66 33 99 67 65
-67 66 34 100 68
-68 67 35 101 69
-69 68 36 102 70
-70 69 37 103 71
-71 70 38 104 72
-72 71 39 105 73
-73 72 40 106 74
-74 73 41 107 75
-75 74 42 108 76
-76 77 75 43 109
-77 44 1 78 76
-78 77 45 2 79
-79 78 46 3 80
-80 79 47 4 81
-81 80 48 5 82
-82 81 49 6 83
-83 82 50 7 84
-84 83 51 8 85
-85 84 52 9 86
-86 85 53 10 87
-87 11 88 86 54
-88 55 12 89 87
-89 88 56 13 90
-90 89 57 14 91
-91 90 58 15 92
-92 91 59 16 93
-93 92 60 17 94
-94 93 61 18 95
-95 94 62 19 96
-96 95 63 20 97
-97 96 64 21 98
-98 22 99 97 65
-99 66 23 100 98
-100 99 67 24 101
-101 100 68 25 102
-102 101 69 26 103
-103 102 70 27 104
-104 103 71 28 105
-105 104 72 29 106
-106 105 73 30 107
-107 106 74 31 108
-108 107 75 32 109
-109 33 1 108 76
0

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