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On this page are computer-accessible forms for the graph C4[ 128, 53 ] = BGCG(KE_16(1,7,2,11,1);K1;{4,6}).

(I) Following is a form readable by MAGMA:

g:=Graph<128|{ {64, 80}, {64, 82}, {64, 114}, {64, 127}, {13, 77}, {20, 84}, {24, 88}, {49, 113}, {53, 117}, {58, 122}, {9, 72}, {31, 94}, {29, 92}, {46, 111}, {60, 125}, {10, 72}, {41, 107}, {48, 114}, {7, 68}, {23, 84}, {24, 91}, {57, 122}, {15, 75}, {39, 99}, {60, 120}, {22, 83}, {26, 95}, {40, 109}, {8, 78}, {15, 73}, {26, 92}, {46, 104}, {53, 115}, {59, 125}, {14, 73}, {34, 101}, {45, 106}, {49, 118}, {15, 71}, {17, 89}, {26, 82}, {44, 100}, {47, 103}, {7, 78}, {39, 110}, {33, 104}, {42, 99}, {50, 123}, {47, 101}, {52, 126}, {27, 80}, {18, 94}, {37, 105}, {56, 116}, {59, 119}, {2, 79}, {43, 102}, {47, 98}, {51, 126}, {8, 70}, {31, 81}, {21, 91}, {44, 98}, {35, 108}, {51, 124}, {3, 83}, {61, 109}, {37, 117}, {17, 65}, {18, 66}, {41, 121}, {46, 126}, {2, 83}, {35, 114}, {30, 79}, {29, 76}, {7, 86}, {48, 97}, {20, 70}, {36, 118}, {23, 69}, {53, 103}, {59, 105}, {25, 74}, {62, 109}, {52, 103}, {58, 105}, {9, 93}, {63, 107}, {13, 89}, {25, 77}, {27, 79}, {55, 99}, {56, 108}, {27, 78}, {62, 107}, {29, 72}, {49, 100}, {57, 108}, {12, 90}, {62, 104}, {38, 112}, {28, 74}, {50, 100}, {12, 91}, {61, 106}, {33, 118}, {32, 119}, {13, 90}, {14, 89}, {17, 70}, {19, 68}, {6, 94}, {7, 95}, {19, 75}, {6, 95}, {34, 123}, {11, 81}, {63, 101}, {38, 124}, {16, 74}, {48, 106}, {58, 96}, {12, 87}, {38, 125}, {14, 85}, {16, 75}, {18, 73}, {22, 77}, {4, 88}, {27, 71}, {40, 116}, {1, 92}, {5, 88}, {12, 81}, {40, 117}, {36, 122}, {37, 123}, {60, 98}, {11, 84}, {35, 124}, {24, 71}, {43, 116}, {6, 102}, {34, 66}, {33, 65}, {30, 126}, {16, 112}, {45, 76}, {49, 80}, {19, 113}, {39, 69}, {52, 86}, {3, 96}, {32, 67}, {5, 102}, {45, 78}, {61, 94}, {20, 112}, {32, 68}, {23, 115}, {56, 92}, {9, 111}, {30, 120}, {50, 84}, {2, 101}, {8, 111}, {22, 113}, {47, 72}, {51, 91}, {1, 104}, {10, 99}, {17, 120}, {26, 115}, {11, 97}, {29, 119}, {21, 127}, {10, 97}, {22, 125}, {54, 93}, {2, 110}, {15, 98}, {63, 82}, {36, 73}, {18, 127}, {20, 122}, {37, 75}, {23, 121}, {57, 87}, {59, 85}, {1, 110}, {33, 81}, {1, 112}, {39, 86}, {3, 114}, {54, 71}, {4, 118}, {36, 86}, {25, 107}, {42, 88}, {4, 119}, {28, 111}, {44, 95}, {48, 67}, {41, 93}, {24, 109}, {54, 67}, {55, 66}, {9, 127}, {53, 67}, {55, 65}, {57, 79}, {54, 65}, {28, 100}, {34, 90}, {31, 103}, {42, 82}, {61, 69}, {52, 77}, {63, 70}, {60, 69}, {3, 121}, {62, 68}, {35, 89}, {32, 90}, {6, 124}, {16, 106}, {56, 66}, {10, 113}, {38, 93}, {21, 110}, {40, 83}, {43, 80}, {44, 87}, {46, 85}, {21, 105}, {28, 96}, {4, 121}, {5, 120}, {8, 117}, {14, 115}, {55, 74}, {5, 123}, {41, 87}, {43, 85}, {50, 76}, {11, 116}, {31, 96}, {30, 97}, {19, 108}, {25, 102}, {51, 76}, {13, 128}, {42, 128}, {45, 128}, {58, 128} }>;

(II) A more general form is to represent the graph as the orbit of {64, 80} under the group generated by the following permutations:

a: (2, 33, 26, 16)(3, 31, 53, 48)(4, 6, 37, 30)(7, 19, 57, 36)(8, 10, 41, 18)(11, 23, 61, 40)(12, 14, 45, 22)(15, 27, 49, 44)(17, 42, 25, 34)(20, 39, 62, 56)(21, 46, 29, 38)(24, 43, 50, 60)(28, 47, 54, 64)(32, 35, 58, 52)(51, 59)(55, 63)(65, 82, 74, 101)(66, 70, 99, 107)(67, 114, 96, 103)(68, 108, 122, 86)(69, 109, 116, 84)(71, 80, 100, 98)(72, 93, 127, 111)(73, 78, 113, 87)(75, 79, 118, 95)(76, 125, 91, 85)(77, 90, 89, 128)(81, 115, 106, 83)(88, 102, 123, 120)(92, 112, 110, 104)(94, 117, 97, 121)(105, 126, 119, 124)
b: (1, 2, 3, 28, 55, 56, 57, 41, 9, 10, 11, 20, 63, 64, 49, 33)(4, 46, 39, 40, 58, 25, 18, 19, 12, 38, 47, 48, 50, 17, 26, 27)(5, 14, 7, 24, 59, 52, 61, 37, 13, 6, 15, 32, 51, 60, 53, 45)(8, 42, 43, 36, 62, 21, 22, 31, 16, 34, 35, 44, 54, 29, 30, 23)(65, 92, 79, 121, 111, 99, 116, 122, 107, 127, 113, 81, 112, 101, 114, 100)(66, 108, 87, 93, 72, 97, 84, 70, 82, 80, 118, 104, 110, 83, 96, 74)(67, 76, 120, 115, 78, 88, 85, 86, 109, 105, 77, 94, 75, 90, 124, 98)(68, 91, 125, 103, 106, 123, 89, 95, 71, 119, 126, 69, 117, 128, 102, 73)
c: (3, 27)(4, 45)(5, 13)(6, 14)(7, 23)(8, 41)(11, 19)(12, 37)(15, 31)(16, 33)(17, 25)(20, 62)(22, 30)(24, 58)(28, 54)(32, 50)(35, 43)(36, 61)(38, 46)(40, 57)(44, 53)(48, 49)(51, 59)(52, 60)(65, 74)(67, 100)(68, 84)(69, 86)(70, 107)(71, 96)(73, 94)(75, 81)(76, 119)(77, 120)(78, 121)(79, 83)(80, 114)(85, 124)(87, 117)(88, 128)(89, 102)(90, 123)(91, 105)(93, 111)(95, 115)(97, 113)(98, 103)(104, 112)(106, 118)(108, 116)(109, 122)(125, 126)

(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[ 128, 53 ]
128
-1 110 112 92 104
-2 110 79 101 83
-3 121 114 83 96
-4 88 121 118 119
-5 88 123 102 120
-6 102 124 94 95
-7 78 68 95 86
-8 78 111 70 117
-9 111 93 72 127
-10 99 113 72 97
-11 81 116 84 97
-12 90 91 81 87
-13 77 89 90 128
-14 89 115 73 85
-15 71 73 75 98
-16 112 106 74 75
-17 89 70 65 120
-18 66 94 127 73
-19 68 113 75 108
-20 122 112 70 84
-21 110 91 105 127
-22 77 113 125 83
-23 121 69 115 84
-24 88 91 71 109
-25 77 102 74 107
-26 92 82 115 95
-27 78 79 80 71
-28 100 111 74 96
-29 92 72 119 76
-30 79 126 97 120
-31 81 103 94 96
-32 67 68 90 119
-33 81 104 118 65
-34 66 90 101 123
-35 89 124 114 108
-36 122 73 118 86
-37 123 105 117 75
-38 112 124 125 93
-39 99 110 69 86
-40 83 116 117 109
-41 121 93 107 87
-42 88 99 82 128
-43 80 102 116 85
-44 100 95 87 98
-45 78 106 128 76
-46 111 104 126 85
-47 101 103 72 98
-48 67 114 106 97
-49 100 80 113 118
-50 100 123 84 76
-51 91 124 126 76
-52 77 103 126 86
-53 67 103 115 117
-54 67 71 93 65
-55 66 99 74 65
-56 66 92 116 108
-57 122 79 108 87
-58 122 105 128 96
-59 125 105 85 119
-60 69 125 98 120
-61 69 94 106 109
-62 68 104 107 109
-63 101 70 82 107
-64 80 114 82 127
-65 33 55 17 54
-66 55 34 56 18
-67 48 53 32 54
-68 7 62 19 32
-69 23 60 39 61
-70 17 8 63 20
-71 24 15 27 54
-72 47 29 9 10
-73 14 36 15 18
-74 55 25 16 28
-75 15 37 16 19
-76 45 50 29 51
-77 22 13 25 52
-78 45 27 7 8
-79 2 57 27 30
-80 27 49 64 43
-81 11 33 12 31
-82 26 63 42 64
-83 22 2 3 40
-84 11 23 50 20
-85 46 14 59 43
-86 36 39 7 52
-87 44 12 57 41
-88 24 4 5 42
-89 13 35 14 17
-90 12 34 13 32
-91 12 24 51 21
-92 1 56 26 29
-93 38 41 9 54
-94 6 61 18 31
-95 44 26 6 7
-96 3 58 28 31
-97 11 48 30 10
-98 44 47 15 60
-99 55 39 42 10
-100 44 49 28 50
-101 34 2 47 63
-102 25 5 6 43
-103 47 52 31 53
-104 33 1 46 62
-105 58 37 59 21
-106 45 48 16 61
-107 25 62 41 63
-108 56 35 57 19
-109 24 61 40 62
-110 1 2 39 21
-111 46 28 8 9
-112 1 16 38 20
-113 22 49 19 10
-114 35 3 48 64
-115 23 14 26 53
-116 11 56 40 43
-117 37 40 8 53
-118 33 36 4 49
-119 4 59 29 32
-120 5 60 17 30
-121 23 3 4 41
-122 57 36 58 20
-123 34 37 5 50
-124 35 38 6 51
-125 22 59 38 60
-126 46 51 30 52
-127 18 9 64 21
-128 45 13 58 42
0

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