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On this page are computer-accessible forms for the graph C4[ 144, 51 ] = SDD(W(18,2)).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {72, 79} under the group generated by the following permutations:

a: (41, 54)
b: (23, 37)(50, 60)(105, 127)(106, 129)(124, 139)(130, 142)
c: (2, 4)(3, 7)(5, 12)(6, 16)(8, 13)(9, 18)(10, 21)(11, 24)(15, 30)(19, 27)(20, 34)(22, 28)(23, 25)(26, 39)(31, 45)(33, 42)(35, 41)(36, 48)(37, 38)(40, 51)(43, 52)(44, 46)(49, 54)(50, 53)(55, 61)(56, 57)(59, 63)(60, 62)(65, 69)(66, 72)(67, 68)(70, 71)(73, 74)(75, 78)(76, 82)(77, 86)(79, 83)(80, 94)(81, 96)(84, 100)(85, 103)(87, 107)(88, 105)(89, 111)(90, 101)(91, 108)(92, 97)(93, 104)(95, 118)(98, 119)(99, 122)(102, 125)(106, 128)(109, 124)(110, 127)(112, 134)(113, 132)(114, 120)(115, 126)(116, 131)(117, 123)(121, 137)(129, 140)(130, 141)(133, 139)(135, 143)(136, 138)(142, 144)
d: (4, 12)(52, 61)(74, 78)(86, 107)(94, 118)(111, 134)
e: (9, 44)
f: (20, 36)
g: (12, 52)
h: (3, 9)(44, 56)(76, 84)(79, 92)(81, 98)(90, 114)
m: (28, 41)(54, 63)(91, 113)(93, 115)(116, 135)(117, 136)
n1: (35, 49)
a1: (16, 30)(45, 69)(82, 96)(100, 119)(105, 124)(127, 139)
b1: (6, 15)(31, 65)(76, 81)(84, 98)(88, 109)(110, 133)
c1: (21, 34)(48, 68)(103, 125)(104, 123)(122, 137)(126, 138)
d1: (22, 35)(49, 59)(104, 126)(108, 132)(123, 138)(131, 143)
e1: (37, 50)
f1: (10, 20)(36, 67)(85, 102)(93, 117)(99, 121)(115, 136)
g1: (27, 42)
h1: (34, 48)
m1: (1, 2)(3, 8)(4, 11)(5, 14)(6, 7)(9, 19)(10, 22)(12, 26)(13, 28)(15, 18)(16, 25)(17, 21)(20, 35)(23, 24)(27, 41)(29, 43)(30, 38)(31, 46)(32, 34)(33, 44)(36, 49)(37, 39)(40, 52)(42, 54)(45, 53)(47, 48)(50, 51)(55, 64)(56, 66)(57, 65)(58, 68)(59, 67)(60, 70)(61, 71)(62, 69)(63, 72)(74, 77)(75, 80)(76, 83)(78, 89)(79, 91)(81, 97)(82, 88)(84, 101)(85, 104)(86, 106)(87, 94)(90, 113)(92, 116)(93, 108)(96, 110)(98, 120)(99, 123)(100, 109)(102, 126)(105, 128)(107, 130)(111, 129)(112, 118)(114, 135)(115, 131)(117, 132)(119, 133)(121, 138)(122, 125)(124, 140)(127, 141)(134, 142)(136, 143)(139, 144)
n2: (8, 19)(33, 66)(83, 101)(91, 116)(97, 120)(113, 135)
a2: (32, 47)
b2: (11, 26)(40, 71)(77, 89)(87, 112)(106, 130)(129, 142)
c2: (13, 27)(42, 72)(79, 90)(92, 114)(108, 131)(132, 143)
d2: (24, 39)(51, 70)(86, 111)(107, 134)(128, 141)(140, 144)
e2: (18, 46)
f2: (7, 18)(46, 57)(82, 100)(83, 97)(96, 119)(101, 120)
g2: (19, 33)
h2: (38, 53)
m2: (39, 51)
n3: (25, 38)(53, 62)(88, 110)(109, 133)(128, 140)(141, 144)
a3: (30, 45)
b3: (14, 29)
c3: (17, 32)(47, 58)(85, 99)(102, 121)(103, 122)(125, 137)
d3: (15, 31)
e3: (26, 40)
f3: (5, 43)

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

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