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On this page are computer-accessible forms for the graph C4[ 128, 12 ] = PX(16,3).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {8, 15} under the group generated by the following permutations:

a: (2, 5)(4, 7)(9, 121)(10, 125)(11, 123)(12, 127)(13, 122)(14, 126)(15, 124)(16, 128)(17, 113)(18, 117)(19, 115)(20, 119)(21, 114)(22, 118)(23, 116)(24, 120)(25, 105)(26, 109)(27, 107)(28, 111)(29, 106)(30, 110)(31, 108)(32, 112)(33, 97)(34, 101)(35, 99)(36, 103)(37, 98)(38, 102)(39, 100)(40, 104)(41, 89)(42, 93)(43, 91)(44, 95)(45, 90)(46, 94)(47, 92)(48, 96)(49, 81)(50, 85)(51, 83)(52, 87)(53, 82)(54, 86)(55, 84)(56, 88)(57, 73)(58, 77)(59, 75)(60, 79)(61, 74)(62, 78)(63, 76)(64, 80)(66, 69)(68, 71)
b: (1, 9, 17, 25, 33, 41, 49, 57, 65, 73, 81, 89, 97, 105, 113, 121)(2, 10, 18, 26, 34, 42, 50, 58, 66, 74, 82, 90, 98, 106, 114, 122)(3, 11, 19, 27, 35, 43, 51, 59, 67, 75, 83, 91, 99, 107, 115, 123)(4, 12, 20, 28, 36, 44, 52, 60, 68, 76, 84, 92, 100, 108, 116, 124)(5, 13, 21, 29, 37, 45, 53, 61, 69, 77, 85, 93, 101, 109, 117, 125)(6, 14, 22, 30, 38, 46, 54, 62, 70, 78, 86, 94, 102, 110, 118, 126)(7, 15, 23, 31, 39, 47, 55, 63, 71, 79, 87, 95, 103, 111, 119, 127)(8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, 128)
c: (81, 82)(83, 84)(85, 86)(87, 88)(89, 91)(90, 92)(93, 95)(94, 96)(97, 101)(98, 102)(99, 103)(100, 104)
d: (17, 18)(19, 20)(21, 22)(23, 24)(25, 27)(26, 28)(29, 31)(30, 32)(33, 37)(34, 38)(35, 39)(36, 40)
e: (49, 50)(51, 52)(53, 54)(55, 56)(57, 59)(58, 60)(61, 63)(62, 64)(65, 69)(66, 70)(67, 71)(68, 72)
f: (105, 106)(107, 108)(109, 110)(111, 112)(113, 115)(114, 116)(117, 119)(118, 120)(121, 125)(122, 126)(123, 127)(124, 128)
g: (73, 74)(75, 76)(77, 78)(79, 80)(81, 83)(82, 84)(85, 87)(86, 88)(89, 93)(90, 94)(91, 95)(92, 96)
h: (41, 42)(43, 44)(45, 46)(47, 48)(49, 51)(50, 52)(53, 55)(54, 56)(57, 61)(58, 62)(59, 63)(60, 64)
m: (9, 10)(11, 12)(13, 14)(15, 16)(17, 19)(18, 20)(21, 23)(22, 24)(25, 29)(26, 30)(27, 31)(28, 32)
n1: (97, 98)(99, 100)(101, 102)(103, 104)(105, 107)(106, 108)(109, 111)(110, 112)(113, 117)(114, 118)(115, 119)(116, 120)
a1: (33, 34)(35, 36)(37, 38)(39, 40)(41, 43)(42, 44)(45, 47)(46, 48)(49, 53)(50, 54)(51, 55)(52, 56)
b1: (65, 66)(67, 68)(69, 70)(71, 72)(73, 75)(74, 76)(77, 79)(78, 80)(81, 85)(82, 86)(83, 87)(84, 88)
c1: (1, 2)(3, 4)(5, 6)(7, 8)(9, 11)(10, 12)(13, 15)(14, 16)(17, 21)(18, 22)(19, 23)(20, 24)
d1: (89, 90)(91, 92)(93, 94)(95, 96)(97, 99)(98, 100)(101, 103)(102, 104)(105, 109)(106, 110)(107, 111)(108, 112)
e1: (25, 26)(27, 28)(29, 30)(31, 32)(33, 35)(34, 36)(37, 39)(38, 40)(41, 45)(42, 46)(43, 47)(44, 48)
f1: (57, 58)(59, 60)(61, 62)(63, 64)(65, 67)(66, 68)(69, 71)(70, 72)(73, 77)(74, 78)(75, 79)(76, 80)
g1: (1, 3)(2, 4)(5, 7)(6, 8)(9, 13)(10, 14)(11, 15)(12, 16)(121, 122)(123, 124)(125, 126)(127, 128)

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

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