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.