Unimodality of the independence polynomial of clique corona graphs

For a positive integer p, a graph G belongs to the class Wp if |V(G)| ≥ p and any p disjoint independent sets can be extended to pdisjoint maximum independent sets. In this paper, we establish several inequalities for the coefficients of the independence polynomial of graphs in Wp. We then prove that the clique corona graph G ∘ Kp, formed from a graph G and a complete graph Kp, also belongs to Wp. As an application, we examine the unimodality problem for the independence polynomial of G ∘ Kp. In particular, we prove that the independence polynomial of Sn ∘ Kp, where Sn is a star graph, is unimodal.