The PI and Edge Szeged Polynomials of an Infinite Family of Fullerenes

Let G be a graph, e = uv ∈ E(G), mu(e) be the number of edges of G lying closer to u than to v and mv(e) be the number of edges of G lying closer to v than to u. Then the PI and edge Szeged polynomials of the graph G are defined as and , respectively. Here, mu(e) is the number of edges of G lying closer to u than to v and mv(e) is the number of edges of G lying closer to v than to u. These counting polynomials for an infinite family of fullerenes are computed.