The topological index of a graph G is a numeric quantity related to G which is invariant under automorphisms of G. In this paper, the vertex PI and Szeged indices of an infinite family of fullerenes are computed.
Let G be a graph, e = uv ∈ E(G), nu(e) be the number of vertices of G lying closer to u than to v and nv(e) be the number of vertices of G lying closer to v than to u. The vertex PI and Szeged polynomials of the graph G are defined as PIv(G,x) = P e=uv x nu(e)+nv (e) and Sz(G,x) = P e=uv x nu(e)nv (e) , respectively. In this paper, these counting polynomials for an infinite family of IPR fullerenes are computed.
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