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On this page are computer-accessible forms for the graph C4[ 136, 7 ] = PS(8,17;4).

(I) Following is a form readable by MAGMA:

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

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

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