Deficiency of a bipartite graph

Deficiency of a bipartite graph --- дефицит двудольного графа.

For a vertex [math]\displaystyle{ v }[/math], the deficiency of a bipartite graph [math]\displaystyle{ D(v) }[/math] is a set of pairs defined by [math]\displaystyle{ D(v) = \{(x,y)| v \in N(x), v \in N(y), x \not \in N(y), x \neq y\} }[/math]. So a vertex [math]\displaystyle{ v }[/math] is simplicial if [math]\displaystyle{ D(v) = \emptyset }[/math].

For an edge [math]\displaystyle{ (x,y) }[/math], the deficiency of a bipartite graph is the set of pairs defined by [math]\displaystyle{ D(x,y) = \{(a,b)| a, b \in N(x) \cup N(y), (a,b) \not \in E\} }[/math]. So an edge [math]\displaystyle{ (x,y) }[/math] is bisimplicial if [math]\displaystyle{ D(x,y) = \emptyset }[/math].

Here [math]\displaystyle{ N(v) }[/math] denotes a neighbourhood of [math]\displaystyle{ v }[/math].