The General Connectivity Indices of Benzenoid Systems and Phenylenes

The general connectivity index R-alpha(G) of a graph G = (V, E) is defined as Sigma(uv is an element of E)(d(u)d(v))(alpha), where d(v) denotes the degree of a vertex v and alpha not equal 0 is a real number. In this paper, we give the expressions for computing the general connectivity indices of benzenoid systems and phenylenes, and a relation between the general connectivity indices of a phenylene and its corresponding hexagonal squeeze, and the extremal values of R-alpha(G) in benzenoid systems with h hexagons for some real numbers alpha.