# Neighborhood Number in Graphs

Volume 5, Issue 4, pp 265 - 270 Publication Date: December 30, 2012
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### 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.

### Keywords

• Neighborhood set
• Neighborhood number
• Jahangir graph
• Harary graphs
• Circulant graph.

•  05C38
•  05C50

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