cograph

English

Etymology

From co- +‎ graph.

Noun

cograph (plural cographs)

1. (mathematics) A graph formed from another by complementation and disjoin union.
2. (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 $\{(1,7),(2,5),(3,3),(4,3),(5,2),(6,4),(7,6),(8,5),(9,7),(10,6),(11,6)\}$, append an apostrophe to the abscissas so that they will not be confused with ordinates when obtaining their disjoint union, which is: $\{2,3,4,5,6,7,1',2',3',4',5',6',7',8',9',10',11'\}$. The cograph then is $\{\{7,1',9'\},\{6,7',10',11'\},\{5,2',8'\},\{4,6'\},\{3,3',4'\},\{2,5'\}\}$.

Derived terms

• cographic