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On this page are computer-accessible forms for the graph C4[ 144, 54 ] = PL(CSI(W(6,2)[6^4],3)).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {65, 95} under the group generated by the following permutations:

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

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

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