Diametral Covering Number of a Graph

Abstract

In this paper, we introduce the diametral covering number of a graph. A subset S of V(G) is said to be a diametral cover for G if every diametral path of G contains at least one vertex of S. The minimum cardinality of S taken over all diametral covers is called the diametral covering number of G and is denoted by σd(G). Here we have given the diametral covering number of several classes of graphs and have given bounds for the same in terms of basic graph parameters. Also, a characterization of graphs having particular diametral covering number is given.