A general modeling of some vertex-degree based topological indices in benzenoid systems and phenylenes
A graph invariant I(G) of a connected graph G = (V, E) contributed by the weights of all edges is defined as I(G) = Sigma c(ij)x(ij) with the summation over all edges, c(ij) is the weight of edges connecting vertices of degree i and j, x(ij) is the number of edges of G connecting vertices of degree i and j. It generalizes Randic index, Zagreb index, sum-connectivity index, GA(1) index, ABC index etc. In this paper, we first give the expressions for computing this invariant I(G) of benzenoid systems and phenylenes, and a relation between this invariant of a phenylene and its corresponding hexagonal squeeze, and then determine the extremal values of I(G) and extremal graphs in catacondensed benzenoid systems and phenylenes, and a unified approach to the extremal values and extremal graphs of Randic index, the general Randic index, Zagreb index, sum-connectivity index, the general sum-connectivity index, GA(1) index and ABC index in benzenoid systems and phenylenes. (C) 2011 Elsevier Ltd. All rights reserved.
benzenoid system phenylene graph invariant extremal graph