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On this page are computer-accessible forms for the graph C4[ 128, 18 ] = PL(LoPr_16(1,8,2,8,1),[4^16,16^4]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {64, 77} under the group generated by the following permutations:

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

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

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