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On this page are computer-accessible forms for the graph C4[ 128, 19 ] = PL(LoPr_16(1,8,2,8,3),[4^16,16^4]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {64, 90} under the group generated by the following permutations:

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

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

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