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On this page are computer-accessible forms for the graph C4[ 128, 42 ] = PL(ATD[8,1]#ATD[8,2]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {64, 69} under the group generated by the following permutations:

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

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

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