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On this page are computer-accessible forms for the graph C4[ 135, 4 ] = PS(15,9;2).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {36, 37} under the group generated by the following permutations:

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

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

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