Neighborhood Number in Graphs


Authors

Z. Tahmasbzadehbaee - Department of Mathematics, University of Mysore, Manasagangotri, Mysore-570 006, India.
N. S. Soner - Department of Mathematics, University of Mysore, Manasagangotri, Mysore-570 006, India.
D. A. Mojdeh - Department of Mathematics, University of Tafresh, Tafresh, Iran.


Abstract

A set \(S\) of points in graph \(G\) is a neighborhood set if \(G=\cup_{\nu\in S}\langle N[\nu]\rangle\) where \(\langle N[\nu]\rangle\) is the subgraph of \(G\) induced by \(\nu\) and all points adjacent to \(\nu\). The neighborhood number, denoted \(n_0(G)\), of \(G\) is the minimum cardinality of a neighborhood set of \(G\). In this paper, we study the neighborhood number of certain graphs.


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