## NEIGHBORHUB NUMBER OF GRAPHS

## NEIGHBORHUB NUMBER OF GRAPHS

*V. Mathad, S. I. Khalaf, V. Raikar*

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## Abstract

Let G be a graph. A neighborhub set (n-hub set) S of G is a set of vertices with the property that for any pair of vertices outside of S, there is a path between them with all intermediate vertices in S and G = S v2S < N[v] >. The neighborhub number(n-hub number) hn(G) is then de ned to be the size of a smallest neighborhub set of G. In this paper, the neighborhub number for several classes of graphs is computed, bounds in terms of other graph parameters are also determined.

## Keywords

Neighborhood number, Connected neighborhood number, Hub number, Total hub number, Neighborhub number.