Split and non-split hub number of graphs

Abstract

A split hub set S in a graph G is a hub set such that the induced subgraph hV \ Si is disconnected. The split hub number of G, denoted by hs(G) is the minimum size of a split hub set in G. In this paper, the split hub number for several classes of graphs is computed and we investigate the relationship of hs(G) with other known parameters of G. Also the concept of non-split hub number is introduced and its exact values for some standard graphs are computed.