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On this page are computer-accessible forms for the graph C4[ 144, 19 ] = PL(MSY(6,12,5,0)).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {64, 85} under the group generated by the following permutations:

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

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

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