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On this page are computer-accessible forms for the graph C4[ 150, 9 ] = PL(ProjLR(3,5)).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {44, 45} under the group generated by the following permutations:

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

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