On Double Signal Number of a Graph

Abstract

A set S of vertices in a connected graph G = (V,E) is called a signal set if every vertex not in S lies on a signal path between two vertices from S. A set S is called a double signal set of G if S if for each pair of vertices x,y ∈ G there exist u,v ∈ S such that x,y ∈ L[u,v]. The double signal number dsn(G) of G is the minimum cardinality of a double signal set. Any double signal set of cardinality dsn(G) is called dsn-set of G. In this paper we introduce and initiate some properties on double signal number of a graph. We have also given relation between geodetic number, signal number and double signal number for some classes of graphs.