Neighborhub number of graphs

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 Uv?S < N[v] >. The neighborhub number (n-hub number) hn(G) is then defined 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.