The Matching Number Condition of a Graph
An L · 1999
Let G be a simple graph. The size of any largest matching in G is called the matching number of G and is denoted by v(G). In this paper, we obtain the following. (1) Let G be connected and incomplete. Then v(G-{x, y})=v(G)-1 for x,y ∈V(G) with xy(?)E(G) if and only if (a) G[A(G)] is complete and each of A(G) is adjacent to every point of C(G). (b) c(D(G)) =|A(G)| + 1. and (c) y∈D(G-x) for x.y∈C(G). (2) Let G be connected and incomplete. Then v(G-{x,y}) = v(G)-2 for x,y ∈V(G) with xy(?) E(G) if and only if G(?)Kn,n. where n (?) 2.