### ON DOUBLE SIGNAL NUMBER OF A GRAPH

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)

#### 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 $$x,y \in G$$ 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.

#### Keywords

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

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