The general connectivity indices of fluoranthene-type benzenoid systems

The general connectivity index Rα(G) of a graph G = ( V , E ) is defined as R α ( G ) = ? ( u , v ) ? E ( G ) ( d u d v ) α , where (u, v) is an edge of G, du and dv denote the degrees of the vertices u and v, respectively, and α ? 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 Rα(G) in f-benzenoid systems with h hexagons for some real number α. Especially, the extremal values of Rα(G) in cata-catacondensed fluoranthene-type benzenoid systems with h hexagons were studied.

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