Hub-integrity polynomial of graphs

Abstract

Graph polynomials are polynomials assigned to graphs. Interestingly, they also arise in many areas outside graph theory as well. Many properties of graph polynomials 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) = ?? i=h hi(G, i)x i , 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 coefficients are obtained. Also, the hub-integrity polynomial of some specific graphs is computed.