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On this page are computer-accessible forms for the graph C4[ 144, 59 ] = PL(CS(DW(6,3)[4^9],1)).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {69, 85} under the group generated by the following permutations:

a: (5, 7)(9, 11)(10, 12)(13, 15)(17, 20)(18, 19)(22, 24)(25, 50)(26, 49)(27, 52)(28, 51)(29, 56)(30, 55)(31, 54)(32, 53)(33, 57)(34, 58)(35, 59)(36, 60)(37, 61)(38, 62)(39, 63)(40, 64)(41, 66)(42, 65)(43, 68)(44, 67)(45, 71)(46, 72)(47, 69)(48, 70)(73, 74)(75, 80)(76, 79)(77, 78)(81, 82)(83, 88)(84, 87)(85, 86)(89, 97)(90, 98)(91, 99)(92, 100)(93, 101)(94, 102)(95, 103)(96, 104)(105, 110)(106, 109)(107, 108)(111, 112)(113, 121)(114, 122)(115, 123)(116, 124)(117, 125)(118, 126)(119, 127)(120, 128)(129, 141)(130, 142)(131, 143)(132, 144)(133, 137)(134, 138)(135, 139)(136, 140)
b: (9, 10)(11, 12)(17, 18)(19, 20)(37, 40)(38, 39)(61, 64)(62, 63)(105, 109)(106, 110)(107, 111)(108, 112)
c: (5, 6)(7, 8)(29, 30)(31, 32)(49, 52)(50, 51)(57, 60)(58, 59)(97, 101)(98, 102)(99, 103)(100, 104)
d: (1, 2)(3, 4)(17, 20)(18, 19)(45, 48)(46, 47)(69, 72)(70, 71)(81, 85)(82, 86)(83, 87)(84, 88)
e: (2, 4)(5, 24, 8, 21)(6, 23, 7, 22)(9, 20)(10, 19)(11, 18)(12, 17)(25, 28, 27, 26)(29, 48)(30, 47)(31, 46)(32, 45)(33, 41, 36, 42)(34, 44, 35, 43)(37, 38)(39, 40)(49, 51)(53, 71, 54, 72)(55, 69, 56, 70)(57, 66)(58, 67)(59, 68)(60, 65)(61, 63)(62, 64)(73, 85)(74, 86)(75, 87)(76, 88)(77, 81)(78, 82)(79, 83)(80, 84)(89, 133, 93, 129)(90, 134, 94, 130)(91, 135, 95, 131)(92, 136, 96, 132)(97, 137)(98, 138)(99, 139)(100, 140)(101, 141)(102, 142)(103, 143)(104, 144)(105, 108)(106, 107)(109, 112)(110, 111)(113, 114)(115, 120)(116, 119)(117, 118)(121, 122)(123, 128)(124, 127)(125, 126)
f: (21, 22)(23, 24)(45, 46)(47, 48)(49, 50)(51, 52)(65, 66)(67, 68)(137, 141)(138, 142)(139, 143)(140, 144)
g: (13, 14)(15, 16)(37, 38)(39, 40)(57, 58)(59, 60)(65, 68)(66, 67)(121, 125)(122, 126)(123, 127)(124, 128)
h: (13, 16)(14, 15)(33, 34)(35, 36)(41, 44)(42, 43)(61, 62)(63, 64)(113, 117)(114, 118)(115, 119)(116, 120)
m: (21, 23)(22, 24)(25, 26)(27, 28)(41, 42)(43, 44)(45, 46)(47, 48)(49, 50)(51, 52)(65, 66)(67, 68)(69, 70)(71, 72)(129, 133)(130, 134)(131, 135)(132, 136)(137, 141)(138, 142)(139, 143)(140, 144)
n1: (5, 8)(6, 7)(13, 16)(14, 15)(25, 28)(26, 27)(33, 35)(34, 36)(41, 44)(42, 43)(53, 54)(55, 56)(61, 62)(63, 64)(89, 93)(90, 94)(91, 95)(92, 96)(113, 117)(114, 118)(115, 119)(116, 120)
a1: (1, 5, 66, 72, 34, 40)(2, 8, 67, 69, 35, 39)(3, 7, 68, 70, 36, 38)(4, 6, 65, 71, 33, 37)(9, 29, 52, 21, 41, 62)(10, 32, 49, 22, 42, 61)(11, 31, 50, 23, 43, 64)(12, 30, 51, 24, 44, 63)(13, 20, 55, 57, 47, 25)(14, 17, 56, 58, 46, 28)(15, 18, 53, 59, 45, 27)(16, 19, 54, 60, 48, 26)(73, 101, 140, 135, 114, 111)(74, 102, 141, 136, 115, 110)(75, 103, 142, 129, 116, 109)(76, 104, 143, 130, 117, 108)(77, 97, 144, 131, 118, 107)(78, 98, 137, 132, 119, 106)(79, 99, 138, 133, 120, 105)(80, 100, 139, 134, 113, 112)(81, 93, 128, 85, 89, 124)(82, 94, 121, 84, 96, 123)(83, 95, 122)(86, 90, 125, 88, 92, 127)(87, 91, 126)

(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.

**************

&Graph
C4[ 144, 59 ]
144
-1 73 74 85 86
-2 81 82 73 74
-3 77 78 81 82
-4 77 78 85 86
-5 89 90 101 102
-6 89 90 97 98
-7 93 94 97 98
-8 101 102 93 94
-9 110 75 76 109
-10 105 106 75 76
-11 79 80 105 106
-12 110 79 80 109
-13 113 114 125 126
-14 121 122 113 114
-15 121 122 117 118
-16 125 126 117 118
-17 111 112 83 84
-18 83 84 107 108
-19 88 107 108 87
-20 88 111 112 87
-21 129 130 141 142
-22 137 138 129 130
-23 133 134 137 138
-24 133 134 141 142
-25 90 134 91 135
-26 90 91 130 131
-27 94 95 130 131
-28 134 135 94 95
-29 103 104 74 75
-30 99 100 74 75
-31 99 78 100 79
-32 78 79 103 104
-33 92 93 118 119
-34 92 114 93 115
-35 89 114 115 96
-36 89 96 118 119
-37 127 106 128 107
-38 123 124 106 107
-39 110 111 123 124
-40 110 111 127 128
-41 136 116 117 129
-42 132 133 116 117
-43 132 133 113 120
-44 113 136 129 120
-45 143 144 82 83
-46 82 83 139 140
-47 139 140 86 87
-48 143 144 86 87
-49 99 143 98 142
-50 99 138 139 98
-51 102 103 138 139
-52 143 102 103 142
-53 77 95 96 76
-54 77 91 92 76
-55 80 91 92 73
-56 80 73 95 96
-57 100 101 126 127
-58 100 122 101 123
-59 122 123 104 97
-60 104 126 127 97
-61 108 119 109 120
-62 115 116 108 109
-63 112 115 105 116
-64 112 105 119 120
-65 144 124 125 137
-66 124 125 140 141
-67 121 128 140 141
-68 121 144 137 128
-69 135 136 84 85
-70 132 84 85 131
-71 88 132 81 131
-72 88 135 81 136
-73 55 1 56 2
-74 1 2 29 30
-75 29 30 9 10
-76 9 53 10 54
-77 3 4 53 54
-78 3 4 31 32
-79 11 12 31 32
-80 11 55 12 56
-81 2 3 71 72
-82 45 2 46 3
-83 45 46 17 18
-84 69 70 17 18
-85 1 69 4 70
-86 1 47 4 48
-87 47 48 19 20
-88 71 72 19 20
-89 35 36 5 6
-90 25 26 5 6
-91 55 25 26 54
-92 33 55 34 54
-93 33 34 7 8
-94 27 28 7 8
-95 56 27 28 53
-96 56 35 36 53
-97 59 60 6 7
-98 49 6 50 7
-99 49 50 30 31
-100 57 58 30 31
-101 57 58 5 8
-102 5 51 8 52
-103 29 51 52 32
-104 59 60 29 32
-105 11 63 64 10
-106 11 37 38 10
-107 37 38 18 19
-108 61 18 62 19
-109 12 61 62 9
-110 12 39 40 9
-111 17 39 40 20
-112 17 63 20 64
-113 44 13 14 43
-114 34 13 35 14
-115 34 35 62 63
-116 62 41 63 42
-117 15 16 41 42
-118 33 36 15 16
-119 33 36 61 64
-120 44 61 64 43
-121 67 68 14 15
-122 14 58 15 59
-123 58 59 38 39
-124 66 38 39 65
-125 66 13 16 65
-126 13 57 16 60
-127 57 37 60 40
-128 67 68 37 40
-129 22 44 41 21
-130 22 26 27 21
-131 26 70 27 71
-132 70 71 42 43
-133 23 24 42 43
-134 23 24 25 28
-135 25 69 28 72
-136 44 69 72 41
-137 22 23 68 65
-138 22 23 50 51
-139 46 47 50 51
-140 66 67 46 47
-141 66 67 24 21
-142 24 49 52 21
-143 45 48 49 52
-144 45 68 48 65
0

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