X. Lenin Xaviour     (Department of Mathematics, Nesamony Memorial Christian College, Marthandam – 629165, Tamil Nadu, India)
S. Ancy Mary     (Department of Mathematics, St. John’s College of Arts and Science, Ammandivilai, Affliated to Manonmaniam Sundaranar University, Abishekapatti, Tirunelveli – 627012, Tamil Nadu, India)


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 \(\mathrm{dsn}\,(G)\) of \(G\) is the minimum cardinality of a double signal set. Any double signal set of cardinality \(\mathrm{dsn}\,(G)\) is called \(\mathrm{dsn}\)-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.


Signal set, Geodetic set, Double signal set, Double signal number.

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DOI: http://dx.doi.org/10.15826/umj.2022.1.007

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