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On this page are computer-accessible forms for the graph C4[ 128, 13 ] = PX(8,4).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {16, 31} under the group generated by the following permutations:

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

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

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