ON DOUBLE SIGNAL NUMBER OF A GRAPH - X. Lenin Xaviour; S. Ancy Mary (Ural Mathematical Journal, 2022)
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 \(x,y \in G\) there exist \(u,v \in S\) such that \(x,y \in L[u,v]\). 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.