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On this page are computer-accessible forms for the graph C4[ 117, 1 ] = C_117(1,53).

(I) Following is a form readable by MAGMA:

g:=Graph<117|{ {2, 3}, {116, 117}, {114, 115}, {112, 113}, {110, 111}, {108, 109}, {106, 107}, {104, 105}, {102, 103}, {100, 101}, {98, 99}, {96, 97}, {94, 95}, {92, 93}, {90, 91}, {88, 89}, {86, 87}, {84, 85}, {40, 41}, {38, 39}, {36, 37}, {34, 35}, {32, 33}, {30, 31}, {28, 29}, {26, 27}, {4, 5}, {6, 7}, {8, 9}, {10, 11}, {12, 13}, {14, 15}, {16, 17}, {18, 19}, {20, 21}, {22, 23}, {24, 25}, {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}, {1, 2}, {113, 114}, {109, 110}, {105, 106}, {101, 102}, {97, 98}, {93, 94}, {89, 90}, {85, 86}, {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}, {77, 78}, {81, 82}, {3, 4}, {115, 116}, {107, 108}, {99, 100}, {91, 92}, {83, 84}, {35, 36}, {27, 28}, {11, 12}, {19, 20}, {43, 44}, {51, 52}, {59, 60}, {67, 68}, {75, 76}, {7, 8}, {103, 104}, {87, 88}, {39, 40}, {23, 24}, {55, 56}, {71, 72}, {15, 16}, {111, 112}, {47, 48}, {79, 80}, {2, 55}, {8, 61}, {10, 63}, {64, 117}, {1, 54}, {9, 62}, {3, 56}, {7, 60}, {4, 57}, {6, 59}, {5, 58}, {95, 96}, {31, 32}, {1, 65}, {40, 104}, {39, 103}, {38, 102}, {37, 101}, {36, 100}, {35, 99}, {34, 98}, {33, 97}, {32, 96}, {31, 95}, {30, 94}, {29, 93}, {28, 92}, {27, 91}, {26, 90}, {25, 89}, {2, 66}, {3, 67}, {4, 68}, {5, 69}, {6, 70}, {7, 71}, {8, 72}, {9, 73}, {10, 74}, {11, 75}, {12, 76}, {13, 77}, {14, 78}, {15, 79}, {16, 80}, {17, 81}, {18, 82}, {19, 83}, {20, 84}, {21, 85}, {22, 86}, {23, 87}, {24, 88}, {41, 105}, {42, 106}, {43, 107}, {44, 108}, {45, 109}, {46, 110}, {47, 111}, {48, 112}, {49, 113}, {50, 114}, {51, 115}, {52, 116}, {53, 117}, {11, 64}, {31, 84}, {27, 80}, {15, 68}, {43, 96}, {47, 100}, {59, 112}, {63, 116}, {12, 65}, {30, 83}, {28, 81}, {14, 67}, {44, 97}, {46, 99}, {60, 113}, {62, 115}, {13, 66}, {29, 82}, {45, 98}, {61, 114}, {16, 69}, {26, 79}, {18, 71}, {24, 77}, {48, 101}, {50, 103}, {56, 109}, {58, 111}, {17, 70}, {25, 78}, {49, 102}, {57, 110}, {19, 72}, {23, 76}, {51, 104}, {55, 108}, {20, 73}, {22, 75}, {52, 105}, {54, 107}, {21, 74}, {53, 106}, {1, 117}, {32, 85}, {40, 93}, {34, 87}, {42, 95}, {33, 86}, {41, 94}, {35, 88}, {39, 92}, {36, 89}, {38, 91}, {37, 90}, {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, 65)(3, 12)(4, 76)(5, 23)(6, 87)(7, 34)(8, 98)(9, 45)(10, 109)(11, 56)(13, 67)(15, 78)(16, 25)(17, 89)(18, 36)(19, 100)(20, 47)(21, 111)(22, 58)(24, 69)(26, 80)(28, 91)(29, 38)(30, 102)(31, 49)(32, 113)(33, 60)(35, 71)(37, 82)(39, 93)(41, 104)(42, 51)(43, 115)(44, 62)(46, 73)(48, 84)(50, 95)(52, 106)(54, 117)(55, 64)(57, 75)(59, 86)(61, 97)(63, 108)(68, 77)(70, 88)(72, 99)(74, 110)(81, 90)(83, 101)(85, 112)(94, 103)(96, 114)(107, 116)
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, 110, 111, 112, 113, 114, 115, 116, 117)
c: (2, 54)(3, 107)(4, 43)(5, 96)(6, 32)(7, 85)(8, 21)(9, 74)(11, 63)(12, 116)(13, 52)(14, 105)(15, 41)(16, 94)(17, 30)(18, 83)(20, 72)(22, 61)(23, 114)(24, 50)(25, 103)(26, 39)(27, 92)(29, 81)(31, 70)(33, 59)(34, 112)(35, 48)(36, 101)(38, 90)(40, 79)(42, 68)(44, 57)(45, 110)(47, 99)(49, 88)(51, 77)(53, 66)(56, 108)(58, 97)(60, 86)(62, 75)(65, 117)(67, 106)(69, 95)(71, 84)(76, 115)(78, 104)(80, 93)(87, 113)(89, 102)(98, 111)

(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[ 117, 1 ]
117
-1 2 117 54 65
-2 55 66 1 3
-3 56 67 2 4
-4 57 68 3 5
-5 58 69 4 6
-6 59 70 5 7
-7 60 71 6 8
-8 61 72 7 9
-9 62 73 8 10
-10 11 63 74 9
-11 12 64 75 10
-12 11 13 65 76
-13 66 77 12 14
-14 67 78 13 15
-15 68 79 14 16
-16 69 80 15 17
-17 70 81 16 18
-18 71 82 17 19
-19 72 83 18 20
-20 73 84 19 21
-21 22 74 85 20
-22 23 75 86 21
-23 22 24 76 87
-24 77 88 23 25
-25 78 89 24 26
-26 79 90 25 27
-27 80 91 26 28
-28 81 92 27 29
-29 82 93 28 30
-30 83 94 29 31
-31 84 95 30 32
-32 33 85 96 31
-33 34 86 97 32
-34 33 35 87 98
-35 88 99 34 36
-36 89 100 35 37
-37 90 101 36 38
-38 91 102 37 39
-39 92 103 38 40
-40 93 104 39 41
-41 94 105 40 42
-42 95 106 41 43
-43 44 96 107 42
-44 45 97 108 43
-45 44 46 98 109
-46 99 110 45 47
-47 100 111 46 48
-48 101 112 47 49
-49 102 113 48 50
-50 103 114 49 51
-51 104 115 50 52
-52 105 116 51 53
-53 106 117 52 54
-54 55 1 107 53
-55 56 2 108 54
-56 55 57 3 109
-57 110 56 58 4
-58 111 57 59 5
-59 112 58 60 6
-60 113 59 61 7
-61 114 60 62 8
-62 115 61 63 9
-63 116 62 64 10
-64 11 117 63 65
-65 66 1 12 64
-66 67 2 13 65
-67 66 68 3 14
-68 67 69 4 15
-69 68 70 5 16
-70 69 71 6 17
-71 70 72 7 18
-72 71 73 8 19
-73 72 74 9 20
-74 73 75 10 21
-75 11 22 74 76
-76 77 12 23 75
-77 78 13 24 76
-78 77 79 14 25
-79 78 80 15 26
-80 79 81 16 27
-81 80 82 17 28
-82 81 83 18 29
-83 82 84 19 30
-84 83 85 20 31
-85 84 86 21 32
-86 22 33 85 87
-87 88 23 34 86
-88 89 24 35 87
-89 88 90 25 36
-90 89 91 26 37
-91 90 92 27 38
-92 91 93 28 39
-93 92 94 29 40
-94 93 95 30 41
-95 94 96 31 42
-96 95 97 32 43
-97 33 44 96 98
-98 99 34 45 97
-99 100 35 46 98
-100 99 101 36 47
-101 100 102 37 48
-102 101 103 38 49
-103 102 104 39 50
-104 103 105 40 51
-105 104 106 41 52
-106 105 107 42 53
-107 106 108 43 54
-108 44 55 107 109
-109 110 45 56 108
-110 111 46 57 109
-111 110 112 47 58
-112 111 113 48 59
-113 112 114 49 60
-114 113 115 50 61
-115 114 116 51 62
-116 115 117 52 63
-117 1 116 53 64
0

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