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On this page are computer-accessible forms for the graph C4[ 128, 4 ] = {4,4}_[16,4].

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

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

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