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On this page are computer-accessible forms for the graph C4[ 128, 20 ] = KE_32(1,15,2,19,1).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {2, 3} under the group generated by the following permutations:

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

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

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