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On this page are computer-accessible forms for the graph C4[ 128, 36 ] = UG(ATD[128,54]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {32, 33} under the group generated by the following permutations:

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

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

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