Noun
(mathematics) A graph formed from another by complementation and disjoin union.
(mathematics) The dual of the graph of a function. It is an ordinate-indexed partition of the disjoint union of the set of abscissas and ordinates of the function.
Given a function whose graph is
{
(
1
,
7
)
,
(
2
,
5
)
,
(
3
,
3
)
,
(
4
,
3
)
,
(
5
,
2
)
,
(
6
,
4
)
,
(
7
,
6
)
,
(
8
,
5
)
,
(
9
,
7
)
,
(
10
,
6
)
,
(
11
,
6
)
}
{\displaystyle \{(1,7),(2,5),(3,3),(4,3),(5,2),(6,4),(7,6),(8,5),(9,7),(10,6),(11,6)\}}
, append an apostrophe to the abscissas so that they will not be confused with ordinates when obtaining their disjoint union, which is:
{
2
,
3
,
4
,
5
,
6
,
7
,
1
′
,
2
′
,
3
′
,
4
′
,
5
′
,
6
′
,
7
′
,
8
′
,
9
′
,
10
′
,
11
′
}
{\displaystyle \{2,3,4,5,6,7,1',2',3',4',5',6',7',8',9',10',11'\}}
. The cograph then is
{
{
7
,
1
′
,
9
′
}
,
{
6
,
7
′
,
10
′
,
11
′
}
,
{
5
,
2
′
,
8
′
}
,
{
4
,
6
′
}
,
{
3
,
3
′
,
4
′
}
,
{
2
,
5
′
}
}
{\displaystyle \{\{7,1',9'\},\{6,7',10',11'\},\{5,2',8'\},\{4,6'\},\{3,3',4'\},\{2,5'\}\}}
.