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On this page are computer-accessible forms for the graph C4[ 128, 51 ] = BGCG({4,4}_8,0;K1;{17,19}).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {64, 92} under the group generated by the following permutations:

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

(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.

**************

&Graph
C4[ 128, 51 ]
128
-1 68 71 93 87
-2 89 94 85 87
-3 121 125 94 97
-4 66 68 114 97
-5 66 89 80 116
-6 121 93 116 84
-7 114 84 85 108
-8 80 125 71 108
-9 122 68 72 128
-10 100 95 128 85
-11 121 102 95 109
-12 99 110 68 109
-13 77 110 100 80
-14 77 121 72 96
-15 99 126 85 96
-16 122 80 102 126
-17 92 82 72 73
-18 100 81 73 107
-19 91 102 83 107
-20 99 82 83 118
-21 100 118 75 65
-22 91 72 117 65
-23 99 112 81 117
-24 112 102 92 75
-25 124 70 82 87
-26 67 81 104 87
-27 67 111 91 97
-28 123 82 115 97
-29 123 104 116 75
-30 90 91 124 116
-31 90 81 115 108
-32 111 70 75 108
-33 122 69 124 74
-34 104 95 74 98
-35 111 79 95 86
-36 110 69 115 86
-37 110 113 104 105
-38 79 113 124 96
-39 115 127 96 98
-40 111 122 105 127
-41 78 69 71 73
-42 101 94 73 98
-43 79 83 94 119
-44 66 69 83 106
-45 66 101 105 65
-46 78 79 84 65
-47 112 84 106 98
-48 112 71 105 119
-49 78 70 128 120
-50 67 101 128 76
-51 88 67 119 109
-52 123 106 109 120
-53 77 101 123 103
-54 77 88 78 90
-55 90 126 106 76
-56 70 103 126 119
-57 92 93 74 120
-58 89 74 107 76
-59 88 125 107 86
-60 114 118 86 120
-61 89 113 103 118
-62 88 113 93 117
-63 114 127 117 76
-64 92 103 125 127
-65 22 45 46 21
-66 44 45 4 5
-67 26 27 50 51
-68 1 12 4 9
-69 33 44 36 41
-70 56 25 49 32
-71 1 48 8 41
-72 22 14 17 9
-73 17 18 41 42
-74 33 34 57 58
-75 24 29 21 32
-76 55 58 50 63
-77 13 14 53 54
-78 46 49 41 54
-79 35 46 38 43
-80 13 5 16 8
-81 23 26 18 31
-82 25 17 28 20
-83 44 19 20 43
-84 46 47 6 7
-85 2 15 7 10
-86 35 36 59 60
-87 1 2 25 26
-88 59 51 62 54
-89 2 58 5 61
-90 55 30 31 54
-91 22 27 19 30
-92 24 57 17 64
-93 1 57 6 62
-94 2 3 42 43
-95 11 34 35 10
-96 14 15 38 39
-97 3 4 27 28
-98 34 47 39 42
-99 12 23 15 20
-100 13 18 10 21
-101 45 50 42 53
-102 11 24 16 19
-103 56 61 53 64
-104 34 26 37 29
-105 45 37 48 40
-106 44 55 47 52
-107 58 59 18 19
-108 7 8 31 32
-109 11 12 51 52
-110 12 13 36 37
-111 35 27 40 32
-112 23 24 47 48
-113 37 38 61 62
-114 4 60 7 63
-115 36 28 39 31
-116 5 6 29 30
-117 22 23 62 63
-118 60 61 20 21
-119 56 48 51 43
-120 57 49 60 52
-121 11 3 14 6
-122 33 16 40 9
-123 28 29 52 53
-124 33 25 38 30
-125 3 59 8 64
-126 55 56 15 16
-127 39 40 63 64
-128 49 50 9 10
0

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