• A THEOREM ON DEGREE OF VERTICES WITH RESPECT TO A VERTEX SET

Abstract

In this short paper, we considered the concept “degree of a vertex with respect to a given vertex set” in simple graphs. We included the necessary fundamentals and examples. Finally we obtained a theorem “If A is a proper subset of a vertex set V(G) of a simple graph G, then the following two conditions are equivalent: (i) =  for all             V(G); and (ii) , where  denotes the degree of v with respect to the given vertex set A”.