HUB-INTEGRITY POLYNOMIAL OF GRAPHS

HUB-INTEGRITY POLYNOMIAL OF GRAPHS

S. S. Mahde, V. Mathad

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Abstract

Graph polynomials are polynomials assigned to graphs. Interestingly, they also arise in many areas outside graph theory as well. Many properties of graph poly- nomials have been widely studied. In this paper, we introduce a new graph polynomial. The hub-integrity polynomial of G is the polynomial HIs(G; x) = Xp i=h hi(G; i)xi; such that hi(G; i) is the number of HI-sets of G of size i, and h is the hub number of G. Some properties of HIs(G; x) and its coecients are obtained. Also, the hub-integrity polynomial of some specic graphs is computed.

Keywords

Integrity, Hub set, Hub-integrity, HI-set of a graph G, HIs-polynomials.