[Home] [Table] [Glossary] [Families]

On this page are computer-accessible forms for the graph C4[ 144, 48 ] = SDD({4,4}_6,0).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {72, 76} under the group generated by the following permutations:

a: (25, 42)
b: (18, 53)
c: (7, 38)
d: (2, 3, 4, 6)(5, 13, 8, 9)(7, 10, 11, 15)(12, 14, 18, 20)(16, 22)(17, 26, 21, 19)(23, 29)(24, 34, 31, 27)(25, 35, 32, 28)(30, 37, 38, 46)(33, 36, 42, 41)(39, 44, 43, 48)(40, 45, 51, 55)(47, 57, 58, 68)(49, 63, 54, 52)(50, 64, 56, 53)(60, 65, 61, 66)(62, 71, 67, 72)(73, 74, 75, 77)(76, 86, 80, 95)(78, 82, 83, 89)(79, 87, 84, 81)(85, 107, 93, 118)(88, 102, 97, 91)(90, 99, 100, 111)(92, 108, 104, 96)(94, 101, 106, 98)(103, 120, 114, 109)(105, 126, 116, 115)(110, 128, 121, 117)(112, 119, 123, 129)(113, 127, 124, 122)(125, 137, 135, 141)(130, 134, 138, 132)(131, 139, 133, 136)(140, 144, 143, 142)
e: (4, 47)
f: (24, 66)
g: (11, 30)
h: (44, 52)
m: (15, 37)
n1: (6, 57)
a1: (32, 33)
b1: (14, 56)
c1: (22, 29)
d1: (9, 67)
e1: (2, 58)
f1: (5, 72)
g1: (13, 62)
h1: (28, 36)
m1: (2, 3)(4, 6)(7, 10)(9, 13)(11, 15)(12, 17)(14, 19)(16, 22)(18, 21)(20, 26)(23, 29)(25, 28)(27, 34)(30, 37)(32, 35)(33, 41)(36, 42)(38, 46)(39, 48)(40, 50)(43, 44)(45, 53)(47, 57)(49, 52)(51, 56)(54, 63)(55, 64)(58, 68)(60, 61)(62, 67)(73, 74)(75, 77)(76, 79)(78, 82)(80, 84)(81, 86)(83, 89)(85, 92)(87, 95)(88, 94)(90, 99)(91, 101)(93, 104)(96, 107)(97, 106)(98, 102)(100, 111)(103, 112)(105, 115)(108, 118)(109, 119)(110, 113)(114, 123)(116, 126)(117, 127)(120, 129)(121, 124)(122, 128)(125, 134)(130, 137)(131, 136)(132, 135)(133, 139)(138, 141)(140, 142)(143, 144)
n2: (34, 60)
a2: (39, 54)
b2: (48, 63)
c2: (17, 55)
d2: (27, 61)
e2: (43, 49)
f2: (16, 23)
g2: (31, 65)
h2: (10, 46)
m2: (1, 2)(3, 5)(4, 7)(6, 9)(8, 12)(10, 14)(11, 16)(13, 19)(15, 21)(17, 24)(18, 25)(20, 27)(22, 28)(23, 30)(26, 32)(29, 36)(31, 39)(33, 40)(34, 43)(35, 44)(37, 45)(38, 47)(41, 52)(42, 53)(46, 56)(48, 59)(49, 60)(50, 61)(51, 62)(54, 65)(55, 66)(57, 67)(58, 69)(63, 70)(64, 71)(68, 72)(74, 76)(75, 78)(77, 81)(80, 85)(82, 88)(83, 90)(84, 91)(86, 94)(87, 96)(89, 98)(92, 103)(93, 105)(97, 109)(99, 110)(101, 112)(102, 113)(106, 117)(108, 116)(111, 122)(114, 125)(118, 129)(119, 130)(120, 131)(121, 132)(123, 133)(126, 136)(127, 137)(134, 140)(139, 142)(141, 143)
n3: (3, 68)
a3: (20, 50)
b3: (19, 51)
c3: (59, 70)
d3: (8, 71)
e3: (26, 40)
f3: (35, 41)
g3: (21, 45)

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

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