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On this page are computer-accessible forms for the graph C4[ 150, 5 ] = PS(10,15;4).

(I) Following is a form readable by MAGMA:

g:=Graph<150|{ {45, 46}, {105, 106}, {27, 31}, {120, 124}, {90, 94}, {89, 93}, {88, 92}, {57, 61}, {58, 62}, {59, 63}, {75, 76}, {20, 31}, {116, 127}, {112, 123}, {84, 95}, {80, 91}, {52, 63}, {87, 91}, {119, 123}, {118, 122}, {117, 121}, {51, 62}, {115, 126}, {113, 124}, {83, 94}, {81, 92}, {32, 46}, {129, 143}, {128, 142}, {97, 111}, {96, 110}, {33, 47}, {64, 78}, {65, 79}, {50, 61}, {135, 136}, {114, 125}, {82, 93}, {1, 17}, {134, 150}, {133, 149}, {132, 148}, {131, 147}, {130, 146}, {129, 145}, {128, 144}, {104, 120}, {103, 119}, {102, 118}, {101, 117}, {100, 116}, {99, 115}, {98, 114}, {97, 113}, {96, 112}, {38, 54}, {37, 53}, {36, 52}, {35, 51}, {34, 50}, {33, 49}, {32, 48}, {14, 30}, {13, 29}, {12, 28}, {11, 27}, {10, 26}, {9, 25}, {8, 24}, {7, 23}, {6, 22}, {5, 21}, {4, 20}, {3, 19}, {2, 18}, {39, 55}, {40, 56}, {41, 57}, {42, 58}, {43, 59}, {44, 60}, {64, 80}, {65, 81}, {66, 82}, {67, 83}, {68, 84}, {69, 85}, {70, 86}, {71, 87}, {72, 88}, {73, 89}, {74, 90}, {2, 16}, {135, 149}, {134, 148}, {131, 145}, {130, 144}, {103, 117}, {102, 116}, {99, 113}, {98, 112}, {39, 53}, {38, 52}, {35, 49}, {34, 48}, {15, 29}, {14, 28}, {11, 25}, {10, 24}, {7, 21}, {6, 20}, {3, 17}, {42, 56}, {43, 57}, {66, 80}, {67, 81}, {70, 84}, {71, 85}, {74, 88}, {75, 89}, {76, 95}, {108, 127}, {107, 126}, {111, 122}, {4, 18}, {133, 147}, {132, 146}, {101, 115}, {100, 114}, {37, 51}, {36, 50}, {13, 27}, {12, 26}, {5, 19}, {44, 58}, {45, 59}, {68, 82}, {69, 83}, {106, 125}, {110, 121}, {8, 22}, {105, 119}, {104, 118}, {9, 23}, {40, 54}, {41, 55}, {72, 86}, {73, 87}, {1, 30}, {15, 16}, {31, 60}, {91, 120}, {78, 104}, {79, 105}, {76, 102}, {77, 103}, {77, 96}, {79, 98}, {78, 97}, {31, 47}, {95, 111}, {94, 110}, {93, 109}, {92, 108}, {91, 107}, {94, 108}, {95, 109}, {16, 35}, {84, 103}, {80, 99}, {24, 43}, {20, 39}, {17, 36}, {87, 98}, {85, 96}, {83, 102}, {81, 100}, {29, 40}, {25, 44}, {23, 34}, {21, 32}, {19, 38}, {92, 106}, {93, 107}, {18, 37}, {86, 97}, {82, 101}, {30, 41}, {26, 45}, {22, 33}, {16, 42}, {17, 43}, {24, 35}, {88, 99}, {28, 39}, {28, 32}, {30, 34}, {29, 33}, {21, 40}, {89, 100}, {85, 104}, {27, 38}, {25, 36}, {23, 42}, {18, 44}, {19, 45}, {22, 41}, {90, 101}, {86, 105}, {26, 37}, {46, 72}, {47, 73}, {61, 90}, {47, 66}, {46, 65}, {61, 77}, {62, 78}, {63, 79}, {62, 76}, {63, 77}, {48, 67}, {52, 71}, {56, 75}, {49, 68}, {51, 70}, {53, 64}, {55, 66}, {50, 69}, {54, 65}, {48, 74}, {49, 75}, {56, 67}, {60, 71}, {60, 64}, {53, 72}, {55, 74}, {57, 68}, {59, 70}, {54, 73}, {58, 69}, {8, 139}, {12, 143}, {12, 136}, {15, 139}, {14, 138}, {13, 137}, {9, 140}, {11, 142}, {10, 141}, {4, 143}, {1, 140}, {7, 138}, {5, 136}, {3, 142}, {2, 141}, {6, 137}, {1, 147}, {4, 150}, {5, 144}, {7, 146}, {2, 148}, {3, 149}, {6, 145}, {8, 147}, {9, 148}, {15, 146}, {13, 144}, {11, 150}, {10, 149}, {14, 145}, {108, 134}, {109, 135}, {109, 128}, {111, 130}, {106, 132}, {107, 133}, {110, 129}, {121, 150}, {121, 137}, {127, 143}, {126, 142}, {125, 141}, {124, 140}, {123, 139}, {122, 138}, {122, 136}, {127, 141}, {126, 140}, {123, 137}, {112, 131}, {116, 135}, {113, 132}, {119, 130}, {117, 128}, {115, 134}, {124, 138}, {125, 139}, {114, 133}, {118, 129}, {120, 131} }>;

(II) A more general form is to represent the graph as the orbit of {45, 46} under the group generated by the following permutations:

a: (2, 15)(3, 14)(4, 13)(5, 12)(6, 11)(7, 10)(8, 9)(17, 30)(18, 29)(19, 28)(20, 27)(21, 26)(22, 25)(23, 24)(32, 45)(33, 44)(34, 43)(35, 42)(36, 41)(37, 40)(38, 39)(47, 60)(48, 59)(49, 58)(50, 57)(51, 56)(52, 55)(53, 54)(62, 75)(63, 74)(64, 73)(65, 72)(66, 71)(67, 70)(68, 69)(77, 90)(78, 89)(79, 88)(80, 87)(81, 86)(82, 85)(83, 84)(92, 105)(93, 104)(94, 103)(95, 102)(96, 101)(97, 100)(98, 99)(107, 120)(108, 119)(109, 118)(110, 117)(111, 116)(112, 115)(113, 114)(122, 135)(123, 134)(124, 133)(125, 132)(126, 131)(127, 130)(128, 129)(137, 150)(138, 149)(139, 148)(140, 147)(141, 146)(142, 145)(143, 144)
b: (2, 101)(3, 36)(4, 121)(5, 71)(7, 91)(8, 41)(9, 126)(10, 61)(12, 96)(13, 31)(14, 131)(15, 66)(16, 82)(18, 117)(19, 52)(20, 137)(21, 87)(23, 107)(24, 57)(25, 142)(26, 77)(28, 112)(29, 47)(30, 147)(32, 98)(34, 133)(35, 68)(37, 103)(39, 123)(40, 73)(42, 93)(44, 128)(45, 63)(46, 79)(48, 114)(50, 149)(51, 84)(53, 119)(55, 139)(56, 89)(58, 109)(60, 144)(62, 95)(64, 130)(67, 100)(69, 135)(72, 105)(74, 125)(78, 111)(80, 146)(83, 116)(85, 136)(88, 106)(90, 141)(94, 127)(99, 132)(104, 122)(110, 143)(115, 148)(120, 138)
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, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150)
d: (1, 16, 31, 46, 61, 76, 91, 106, 121, 136)(2, 20, 32, 50, 62, 80, 92, 110, 122, 140)(3, 24, 33, 54, 63, 84, 93, 114, 123, 144)(4, 28, 34, 58, 64, 88, 94, 118, 124, 148)(5, 17, 35, 47, 65, 77, 95, 107, 125, 137)(6, 21, 36, 51, 66, 81, 96, 111, 126, 141)(7, 25, 37, 55, 67, 85, 97, 115, 127, 145)(8, 29, 38, 59, 68, 89, 98, 119, 128, 149)(9, 18, 39, 48, 69, 78, 99, 108, 129, 138)(10, 22, 40, 52, 70, 82, 100, 112, 130, 142)(11, 26, 41, 56, 71, 86, 101, 116, 131, 146)(12, 30, 42, 60, 72, 90, 102, 120, 132, 150)(13, 19, 43, 49, 73, 79, 103, 109, 133, 139)(14, 23, 44, 53, 74, 83, 104, 113, 134, 143)(15, 27, 45, 57, 75, 87, 105, 117, 135, 147)

(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[ 150, 5 ]
150
-1 147 17 30 140
-2 16 148 18 141
-3 17 149 19 142
-4 143 18 150 20
-5 144 136 19 21
-6 22 145 137 20
-7 23 146 138 21
-8 22 24 147 139
-9 23 25 148 140
-10 24 26 149 141
-11 25 27 150 142
-12 143 26 136 28
-13 144 27 137 29
-14 145 28 138 30
-15 146 16 29 139
-16 2 35 15 42
-17 1 3 36 43
-18 44 2 4 37
-19 45 3 5 38
-20 4 6 39 31
-21 5 7 40 32
-22 33 6 8 41
-23 34 7 9 42
-24 35 8 10 43
-25 11 44 36 9
-26 12 45 37 10
-27 11 13 38 31
-28 12 14 39 32
-29 33 13 15 40
-30 1 34 14 41
-31 47 27 60 20
-32 46 48 28 21
-33 22 47 49 29
-34 23 48 50 30
-35 24 16 49 51
-36 25 17 50 52
-37 26 18 51 53
-38 27 19 52 54
-39 55 28 20 53
-40 56 29 21 54
-41 22 55 57 30
-42 23 56 58 16
-43 24 57 59 17
-44 25 58 60 18
-45 46 26 59 19
-46 45 72 32 65
-47 33 66 73 31
-48 34 67 74 32
-49 33 35 68 75
-50 34 36 69 61
-51 35 37 70 62
-52 36 38 71 63
-53 37 39 72 64
-54 38 40 73 65
-55 66 39 41 74
-56 67 40 42 75
-57 68 61 41 43
-58 44 69 62 42
-59 45 70 63 43
-60 44 71 31 64
-61 77 57 90 50
-62 78 58 51 76
-63 77 79 59 52
-64 78 80 60 53
-65 46 79 81 54
-66 55 47 80 82
-67 56 48 81 83
-68 57 49 82 84
-69 58 50 83 85
-70 59 51 84 86
-71 60 52 85 87
-72 88 46 53 86
-73 89 47 54 87
-74 55 88 90 48
-75 56 89 49 76
-76 102 62 95 75
-77 103 61 63 96
-78 104 62 64 97
-79 105 63 65 98
-80 66 99 91 64
-81 67 100 92 65
-82 66 68 101 93
-83 67 69 102 94
-84 68 70 103 95
-85 69 71 104 96
-86 70 72 105 97
-87 91 71 73 98
-88 99 92 72 74
-89 100 93 73 75
-90 101 61 94 74
-91 80 107 87 120
-92 88 81 106 108
-93 89 82 107 109
-94 110 90 83 108
-95 111 84 76 109
-96 77 110 112 85
-97 78 111 113 86
-98 79 112 114 87
-99 88 80 113 115
-100 89 81 114 116
-101 90 82 115 117
-102 83 116 118 76
-103 77 84 117 119
-104 78 85 118 120
-105 79 106 86 119
-106 132 92 125 105
-107 133 91 93 126
-108 134 92 94 127
-109 135 93 95 128
-110 121 94 96 129
-111 122 95 97 130
-112 123 96 98 131
-113 99 132 124 97
-114 100 133 125 98
-115 99 101 134 126
-116 100 102 135 127
-117 121 101 103 128
-118 122 102 104 129
-119 123 103 105 130
-120 91 124 104 131
-121 110 137 117 150
-122 111 136 138 118
-123 112 137 139 119
-124 113 138 140 120
-125 114 106 139 141
-126 115 107 140 142
-127 143 116 108 141
-128 144 117 109 142
-129 110 143 145 118
-130 111 144 146 119
-131 112 145 147 120
-132 113 146 148 106
-133 114 147 149 107
-134 115 148 150 108
-135 136 116 149 109
-136 12 122 135 5
-137 121 13 123 6
-138 122 14 124 7
-139 123 15 125 8
-140 1 124 126 9
-141 2 125 127 10
-142 11 3 126 128
-143 12 4 127 129
-144 13 5 128 130
-145 14 6 129 131
-146 132 15 7 130
-147 1 133 8 131
-148 132 2 134 9
-149 133 3 135 10
-150 11 121 134 4
0

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