Unimodality of the independence polynomial of clique corona graphs

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