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On this page are computer-accessible forms for the graph C4[ 144, 57 ] = PL(CS(DW(6,3)[6^6],1)).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {72, 73} under the group generated by the following permutations:

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

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

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