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On this page are computer-accessible forms for the graph C4[ 144, 55 ] = PL(CS(W(9,2)[9^4],0)).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {66, 95} under the group generated by the following permutations:

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

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

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