Some Relations between Kekule Structure and Morgan-Voyce Polynomials

In this paper, Kekule structures of benzenoid chains are considered. It has been shown that the coefficients of a B-n (x) Morgan Voyce polynomial equal to the number of k-matchings (m(G, k)) of a path graph which has N = 2n + 1 points. Furtermore, two relations are obtained between regularly zig zag non-branched catacondensed benzenoid chains and Morgan Voyce polynomials and between regularly zig zag non branched catacondensed benzenoid chains and their corresponding caterpillar trees. (C) 2017 University of Kashan Press. All rights reserved