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On this page are computer-accessible forms for the graph C4[ 120, 27 ] = KE_30(1,3,10,13,11).

(I) Following is a form readable by MAGMA:

g:=Graph<120|{ {2, 3}, {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}, {1, 2}, {29, 30}, {5, 6}, {9, 10}, {13, 14}, {17, 18}, {21, 22}, {25, 26}, {3, 4}, {27, 28}, {11, 12}, {19, 20}, {52, 62}, {53, 63}, {96, 107}, {100, 111}, {97, 108}, {99, 110}, {51, 61}, {7, 8}, {23, 24}, {98, 109}, {96, 115}, {100, 119}, {97, 116}, {109, 120}, {103, 114}, {99, 118}, {101, 112}, {98, 117}, {102, 113}, {4, 31}, {108, 119}, {104, 115}, {101, 120}, {107, 118}, {105, 116}, {32, 62}, {33, 63}, {64, 94}, {65, 95}, {1, 30}, {106, 117}, {15, 16}, {31, 61}, {66, 96}, {67, 97}, {70, 100}, {71, 101}, {74, 104}, {75, 105}, {78, 108}, {79, 109}, {82, 112}, {83, 113}, {86, 116}, {87, 117}, {90, 120}, {5, 32}, {29, 56}, {7, 34}, {13, 40}, {15, 42}, {21, 48}, {23, 50}, {68, 98}, {69, 99}, {76, 106}, {77, 107}, {84, 114}, {85, 115}, {6, 33}, {30, 57}, {14, 41}, {22, 49}, {8, 35}, {28, 55}, {12, 39}, {24, 51}, {9, 36}, {27, 54}, {25, 52}, {11, 38}, {93, 112}, {95, 114}, {72, 102}, {73, 103}, {88, 118}, {89, 119}, {10, 37}, {26, 53}, {94, 113}, {92, 111}, {91, 110}, {93, 104}, {95, 106}, {94, 105}, {2, 59}, {1, 58}, {16, 43}, {20, 47}, {92, 103}, {1, 61}, {2, 62}, {3, 63}, {17, 44}, {19, 46}, {91, 102}, {80, 110}, {81, 111}, {3, 60}, {18, 45}, {4, 64}, {30, 90}, {29, 89}, {28, 88}, {5, 65}, {6, 66}, {7, 67}, {12, 72}, {13, 73}, {14, 74}, {15, 75}, {20, 80}, {21, 81}, {22, 82}, {23, 83}, {32, 105}, {38, 111}, {36, 109}, {34, 107}, {33, 106}, {37, 110}, {8, 68}, {27, 87}, {26, 86}, {25, 85}, {9, 69}, {10, 70}, {11, 71}, {24, 84}, {35, 108}, {53, 96}, {55, 98}, {39, 112}, {47, 120}, {54, 97}, {31, 71}, {40, 113}, {44, 117}, {42, 115}, {46, 119}, {41, 114}, {45, 118}, {56, 99}, {60, 103}, {16, 76}, {17, 77}, {18, 78}, {19, 79}, {57, 100}, {59, 102}, {43, 116}, {58, 101}, {34, 64}, {43, 73}, {42, 72}, {39, 69}, {38, 68}, {35, 65}, {46, 76}, {47, 77}, {50, 80}, {51, 81}, {54, 84}, {55, 85}, {58, 88}, {59, 89}, {62, 92}, {63, 93}, {36, 66}, {45, 75}, {44, 74}, {37, 67}, {52, 82}, {53, 83}, {60, 90}, {61, 91}, {32, 72}, {39, 79}, {38, 78}, {37, 77}, {36, 76}, {35, 75}, {34, 74}, {33, 73}, {48, 88}, {49, 89}, {50, 90}, {48, 91}, {52, 95}, {49, 92}, {51, 94}, {40, 70}, {41, 71}, {56, 86}, {57, 87}, {50, 93}, {54, 64}, {55, 65}, {31, 104}, {40, 80}, {44, 84}, {43, 83}, {42, 82}, {41, 81}, {45, 85}, {46, 86}, {47, 87}, {56, 66}, {57, 67}, {60, 70}, {48, 78}, {49, 79}, {58, 68}, {59, 69} }>;

(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, 30)(3, 29)(4, 28)(5, 27)(6, 26)(7, 25)(8, 24)(9, 23)(10, 22)(11, 21)(12, 20)(13, 19)(14, 18)(15, 17)(31, 88)(32, 87)(33, 86)(34, 85)(35, 84)(36, 83)(37, 82)(38, 81)(39, 80)(40, 79)(41, 78)(42, 77)(43, 76)(44, 75)(45, 74)(46, 73)(47, 72)(48, 71)(49, 70)(50, 69)(51, 68)(52, 67)(53, 66)(54, 65)(55, 64)(56, 63)(57, 62)(58, 61)(59, 90)(60, 89)(91, 101)(92, 100)(93, 99)(94, 98)(95, 97)(102, 120)(103, 119)(104, 118)(105, 117)(106, 116)(107, 115)(108, 114)(109, 113)(110, 112)
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, 118, 119, 120)
c: (2, 61)(3, 31)(5, 64)(6, 34)(8, 67)(9, 37)(11, 70)(12, 40)(14, 73)(15, 43)(17, 76)(18, 46)(20, 79)(21, 49)(23, 82)(24, 52)(26, 85)(27, 55)(29, 88)(30, 58)(32, 94)(33, 74)(35, 97)(36, 77)(38, 100)(39, 80)(41, 103)(42, 83)(44, 106)(45, 86)(47, 109)(48, 89)(50, 112)(51, 62)(53, 115)(54, 65)(56, 118)(57, 68)(59, 91)(60, 71)(63, 104)(66, 107)(69, 110)(72, 113)(75, 116)(78, 119)(81, 92)(84, 95)(87, 98)(90, 101)

(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[ 120, 27 ]
120
-1 2 58 61 30
-2 1 3 59 62
-3 2 4 60 63
-4 3 5 31 64
-5 4 6 32 65
-6 33 66 5 7
-7 34 67 6 8
-8 35 68 7 9
-9 36 69 8 10
-10 11 37 70 9
-11 12 38 71 10
-12 11 13 39 72
-13 12 14 40 73
-14 13 15 41 74
-15 14 16 42 75
-16 15 17 43 76
-17 44 77 16 18
-18 45 78 17 19
-19 46 79 18 20
-20 47 80 19 21
-21 22 48 81 20
-22 23 49 82 21
-23 22 24 50 83
-24 23 25 51 84
-25 24 26 52 85
-26 25 27 53 86
-27 26 28 54 87
-28 55 88 27 29
-29 56 89 28 30
-30 1 57 90 29
-31 4 71 104 61
-32 5 72 105 62
-33 6 73 106 63
-34 7 74 107 64
-35 8 75 108 65
-36 66 9 76 109
-37 77 110 67 10
-38 11 78 111 68
-39 12 79 112 69
-40 13 80 113 70
-41 14 81 114 71
-42 15 82 115 72
-43 16 83 116 73
-44 17 84 117 74
-45 18 85 118 75
-46 19 86 119 76
-47 77 20 87 120
-48 88 78 91 21
-49 22 89 79 92
-50 23 90 80 93
-51 24 81 61 94
-52 25 82 62 95
-53 26 83 63 96
-54 27 84 64 97
-55 28 85 65 98
-56 66 99 29 86
-57 67 100 30 87
-58 88 1 68 101
-59 89 2 69 102
-60 90 3 70 103
-61 1 91 51 31
-62 2 92 52 32
-63 33 3 93 53
-64 34 4 94 54
-65 55 35 5 95
-66 56 36 6 96
-67 57 37 7 97
-68 58 38 8 98
-69 99 59 39 9
-70 100 60 40 10
-71 11 101 41 31
-72 12 102 42 32
-73 33 13 103 43
-74 44 34 14 104
-75 45 35 15 105
-76 46 36 16 106
-77 47 37 17 107
-78 48 38 18 108
-79 49 39 19 109
-80 110 50 40 20
-81 111 51 41 21
-82 22 112 52 42
-83 23 113 53 43
-84 44 24 114 54
-85 55 45 25 115
-86 56 46 26 116
-87 57 47 27 117
-88 58 48 28 118
-89 59 49 29 119
-90 60 50 30 120
-91 110 102 48 61
-92 111 103 49 62
-93 112 104 50 63
-94 113 105 51 64
-95 114 106 52 65
-96 66 115 107 53
-97 67 116 108 54
-98 55 68 117 109
-99 110 56 69 118
-100 111 57 70 119
-101 112 58 71 120
-102 91 113 59 72
-103 92 114 60 73
-104 93 115 74 31
-105 94 116 75 32
-106 33 95 117 76
-107 77 34 96 118
-108 78 35 97 119
-109 79 36 98 120
-110 99 80 91 37
-111 100 81 92 38
-112 101 82 93 39
-113 102 83 94 40
-114 103 84 95 41
-115 104 85 96 42
-116 105 86 97 43
-117 44 106 87 98
-118 88 99 45 107
-119 89 100 46 108
-120 90 101 47 109
0

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