THE ROOTS OF THE CLIQUE POLYNOMIAL OF A K 4 - FREE CONNECTED PLANAR CHORDAL GRAPH

The clique polynomial of a graph G is the polynomial C(G, x) := P U⊆V (G) x |U| , where the sum runs over all induced subgraphs G[U] that are cliques in G. Hajiabolhasan and Mehrabadi showed that the clique polynomial of any simple graph has a real root. Moreover, they proved that the roots of the clique polynomial of a triangle - free graph are real. In this talk, we present an extension of their result by showing that the roots of the clique polynomial of a K 4 - free connected planar chordal graph are real. We conclude our paper with several open questions and conjectures.