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On this page are computer-accessible forms for the graph C4[ 136, 6 ] = PS(8,17;3).

(I) Following is a form readable by MAGMA:

g:=Graph<136|{ {17, 18}, {32, 35}, {82, 86}, {83, 87}, {33, 36}, {98, 103}, {34, 37}, {64, 71}, {48, 56}, {51, 59}, {50, 58}, {49, 57}, {48, 57}, {50, 59}, {65, 72}, {67, 74}, {64, 74}, {65, 75}, {68, 78}, {49, 58}, {66, 73}, {99, 104}, {84, 88}, {85, 89}, {96, 108}, {97, 109}, {98, 110}, {99, 111}, {80, 93}, {82, 95}, {100, 105}, {102, 107}, {32, 46}, {119, 121}, {118, 120}, {33, 47}, {66, 76}, {67, 77}, {51, 60}, {68, 75}, {81, 94}, {101, 106}, {112, 127}, {2, 18}, {3, 19}, {4, 20}, {5, 21}, {6, 22}, {7, 23}, {8, 24}, {9, 25}, {10, 26}, {11, 27}, {12, 28}, {13, 29}, {14, 30}, {15, 31}, {105, 120}, {107, 122}, {109, 124}, {111, 126}, {1, 19}, {34, 48}, {4, 22}, {5, 23}, {8, 26}, {9, 27}, {12, 30}, {13, 31}, {75, 88}, {79, 92}, {104, 123}, {106, 121}, {108, 127}, {110, 125}, {100, 112}, {101, 113}, {102, 114}, {72, 93}, {74, 95}, {76, 89}, {78, 91}, {105, 124}, {107, 126}, {2, 20}, {3, 21}, {10, 28}, {11, 29}, {96, 118}, {97, 119}, {47, 56}, {73, 94}, {77, 90}, {106, 125}, {108, 123}, {44, 52}, {47, 55}, {46, 54}, {45, 53}, {36, 61}, {46, 55}, {44, 53}, {38, 63}, {36, 62}, {37, 63}, {37, 62}, {45, 54}, {71, 92}, {70, 91}, {74, 87}, {103, 122}, {6, 24}, {35, 61}, {7, 25}, {35, 60}, {43, 52}, {69, 90}, {73, 86}, {19, 50}, {70, 100}, {71, 101}, {1, 34}, {18, 49}, {87, 116}, {86, 115}, {69, 99}, {20, 51}, {90, 112}, {91, 113}, {94, 116}, {95, 117}, {75, 96}, {79, 100}, {28, 48}, {31, 51}, {30, 50}, {29, 49}, {76, 97}, {78, 99}, {88, 117}, {90, 119}, {14, 32}, {15, 33}, {72, 102}, {92, 114}, {93, 115}, {77, 98}, {89, 118}, {16, 32}, {17, 33}, {16, 34}, {31, 45}, {30, 44}, {22, 36}, {23, 37}, {26, 40}, {27, 41}, {83, 96}, {18, 38}, {27, 47}, {19, 39}, {24, 44}, {25, 45}, {26, 46}, {92, 104}, {93, 105}, {94, 106}, {95, 107}, {80, 101}, {84, 97}, {21, 35}, {29, 43}, {28, 42}, {88, 110}, {89, 111}, {81, 102}, {85, 98}, {86, 108}, {87, 109}, {20, 40}, {21, 41}, {22, 42}, {23, 43}, {91, 103}, {24, 38}, {25, 39}, {53, 80}, {55, 82}, {38, 64}, {39, 65}, {39, 64}, {54, 81}, {56, 80}, {61, 85}, {60, 84}, {59, 83}, {58, 82}, {57, 81}, {40, 65}, {42, 67}, {40, 66}, {41, 67}, {41, 66}, {56, 83}, {16, 124}, {17, 125}, {57, 84}, {42, 68}, {43, 68}, {58, 85}, {8, 121}, {10, 123}, {12, 125}, {14, 127}, {9, 122}, {13, 126}, {12, 120}, {13, 121}, {14, 122}, {15, 123}, {62, 72}, {63, 73}, {11, 124}, {52, 76}, {55, 79}, {54, 78}, {53, 77}, {63, 70}, {60, 70}, {61, 71}, {52, 79}, {62, 69}, {2, 127}, {59, 69}, {1, 126}, {7, 120}, {1, 131}, {4, 134}, {5, 135}, {3, 128}, {7, 132}, {11, 136}, {4, 129}, {6, 131}, {2, 132}, {3, 133}, {5, 130}, {8, 133}, {10, 135}, {6, 136}, {9, 134}, {15, 128}, {16, 129}, {17, 130}, {103, 135}, {104, 136}, {109, 128}, {111, 130}, {110, 129}, {113, 128}, {119, 134}, {117, 132}, {115, 130}, {112, 131}, {118, 133}, {116, 135}, {114, 129}, {113, 132}, {115, 134}, {114, 133}, {116, 131}, {117, 136} }>;

(II) A more general form is to represent the graph as the orbit of {17, 18} under the group generated by the following permutations:

a: (1, 18, 35, 52, 69, 86, 103, 120)(2, 32, 44, 59, 82, 98, 118, 126, 17, 21, 43, 62, 73, 91, 105, 131)(3, 29, 36, 66, 78, 93, 116, 132, 16, 24, 51, 55, 77, 96, 107, 125)(4, 26, 45, 56, 74, 88, 114, 121, 15, 27, 42, 65, 81, 101, 109, 136)(5, 23, 37, 63, 70, 100, 112, 127, 14, 30, 50, 58, 85, 89, 111, 130)(6, 20, 46, 53, 83, 95, 110, 133, 13, 33, 41, 68, 72, 94, 113, 124)(7, 34, 38, 60, 79, 90, 108, 122, 12, 19, 49, 61, 76, 99, 115, 135)(8, 31, 47, 67, 75, 102, 106, 128, 11, 22, 40, 54, 80, 87, 117, 129)(9, 28, 39, 57, 71, 97, 104, 134, 10, 25, 48, 64, 84, 92, 119, 123)
b: (2, 17)(3, 16)(4, 15)(5, 14)(6, 13)(7, 12)(8, 11)(9, 10)(19, 34)(20, 33)(21, 32)(22, 31)(23, 30)(24, 29)(25, 28)(26, 27)(36, 51)(37, 50)(38, 49)(39, 48)(40, 47)(41, 46)(42, 45)(43, 44)(53, 68)(54, 67)(55, 66)(56, 65)(57, 64)(58, 63)(59, 62)(60, 61)(70, 85)(71, 84)(72, 83)(73, 82)(74, 81)(75, 80)(76, 79)(77, 78)(87, 102)(88, 101)(89, 100)(90, 99)(91, 98)(92, 97)(93, 96)(94, 95)(104, 119)(105, 118)(106, 117)(107, 116)(108, 115)(109, 114)(110, 113)(111, 112)(121, 136)(122, 135)(123, 134)(124, 133)(125, 132)(126, 131)(127, 130)(128, 129)
c: (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, 129, 130, 131, 132, 133, 134, 135, 136)

(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[ 136, 6 ]
136
-1 34 126 19 131
-2 132 127 18 20
-3 133 128 19 21
-4 22 134 129 20
-5 23 135 130 21
-6 22 24 136 131
-7 132 23 25 120
-8 121 133 24 26
-9 122 134 25 27
-10 123 135 26 28
-11 124 136 27 29
-12 125 28 30 120
-13 121 126 29 31
-14 122 127 30 32
-15 33 123 128 31
-16 34 124 129 32
-17 33 125 18 130
-18 2 38 49 17
-19 1 3 39 50
-20 2 4 40 51
-21 35 3 5 41
-22 36 4 6 42
-23 37 5 7 43
-24 44 38 6 8
-25 45 39 7 9
-26 46 40 8 10
-27 11 47 41 9
-28 12 48 42 10
-29 11 13 49 43
-30 44 12 14 50
-31 45 13 15 51
-32 35 46 14 16
-33 36 47 15 17
-34 1 37 48 16
-35 60 61 21 32
-36 22 33 61 62
-37 23 34 62 63
-38 24 18 63 64
-39 25 19 64 65
-40 66 26 20 65
-41 66 67 27 21
-42 22 67 68 28
-43 23 68 29 52
-44 24 30 52 53
-45 25 31 53 54
-46 55 26 32 54
-47 33 55 56 27
-48 34 56 57 28
-49 57 58 18 29
-50 58 59 19 30
-51 59 60 20 31
-52 44 79 43 76
-53 44 77 45 80
-54 45 78 46 81
-55 46 79 47 82
-56 47 80 48 83
-57 48 81 49 84
-58 49 82 50 85
-59 69 50 83 51
-60 35 70 51 84
-61 35 36 71 85
-62 36 69 37 72
-63 37 70 38 73
-64 38 71 39 74
-65 39 72 40 75
-66 40 73 41 76
-67 77 41 74 42
-68 78 42 75 43
-69 99 90 59 62
-70 100 91 60 63
-71 101 92 61 64
-72 102 93 62 65
-73 66 94 63 86
-74 67 95 64 87
-75 88 68 96 65
-76 66 89 52 97
-77 67 90 53 98
-78 99 68 91 54
-79 55 100 92 52
-80 56 101 93 53
-81 57 102 94 54
-82 55 58 95 86
-83 56 59 96 87
-84 88 57 60 97
-85 89 58 61 98
-86 82 115 73 108
-87 83 116 74 109
-88 110 84 117 75
-89 111 85 118 76
-90 77 112 69 119
-91 78 113 70 103
-92 79 114 71 104
-93 80 115 72 105
-94 81 116 73 106
-95 82 117 74 107
-96 83 118 75 108
-97 84 119 76 109
-98 77 110 103 85
-99 78 111 69 104
-100 79 112 70 105
-101 80 113 71 106
-102 81 114 72 107
-103 122 91 135 98
-104 99 123 92 136
-105 100 124 93 120
-106 121 101 125 94
-107 122 102 126 95
-108 123 127 96 86
-109 124 128 97 87
-110 88 125 129 98
-111 99 89 126 130
-112 100 90 127 131
-113 132 101 91 128
-114 133 102 92 129
-115 134 93 86 130
-116 135 94 87 131
-117 88 132 136 95
-118 89 133 96 120
-119 121 90 134 97
-120 12 105 7 118
-121 13 106 8 119
-122 14 103 107 9
-123 15 104 108 10
-124 11 16 105 109
-125 110 12 17 106
-126 1 111 13 107
-127 2 112 14 108
-128 3 113 15 109
-129 110 4 114 16
-130 111 5 115 17
-131 1 112 6 116
-132 2 113 7 117
-133 3 114 8 118
-134 4 115 9 119
-135 103 5 116 10
-136 11 104 6 117
0

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