The general connectivity indices of fluoranthene-type benzenoid systems

The general connectivity index R-alpha(G) of a graph G = (V,E) is defined as R-alpha(G) = Sigma((dudv)alpha)((u,v)is an element of E(G)), where (u, v) is an edge of G, d(u) and d(v) denote the degrees of the vertices u and v, respectively, and alpha not equal 0 is an arbitrary real number. In this paper, we give the expressions for computing the general connectivity indices of fluoranthene-type benzenoid systems, and we determine the extremal values of R-alpha(G) in f-benzenoid systems with h hexagons for some real number alpha. Especially, the extremal values of R-alpha(G) in cata-catacondensed fluoranthene-type benzenoid systems with h hexagons were studied. (C) 2015 Elsevier Inc. All rights reserved.