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On this page are computer-accessible forms for the graph C4[ 128, 27 ] = PL(BC_32({0,16},{1,7}).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {36, 37} under the group generated by the following permutations:

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

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

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