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On this page are computer-accessible forms for the graph C4[ 128, 52 ] = BGCG(KE_16(1,7,2,11,1);K1;{3,5,9,10}).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {64, 84} under the group generated by the following permutations:

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

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

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