Neighborhood Number in Graphs

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Authors
Z. Tahmasbzadehbaee
 Department of Mathematics, University of Mysore, Manasagangotri, Mysore570 006, India.
N. S. Soner
 Department of Mathematics, University of Mysore, Manasagangotri, Mysore570 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.
Keywords
 Neighborhood set
 Neighborhood number
 Jahangir graph
 Harary graphs
 Circulant graph.
MSC
References

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