The Forcing Vertex Monophonic Number of a Graph

By a graph G = (V,E) we mean a finite undirected connected graph without loops or multiple edges. The order and size of G are denoted by p and q respectively. For basic graph theoretic terminology we refer to Harary.For vertices x and y in a connected graph G, the distance d(x, y) is the length of a shortest x − y path in G.