Extremal double hexagonal chains with respect to k-matchings and k-independent sets

Abstract

“Double hexagonal chains” can be considered as benzenoids constructed by successive fusions of successive naphthalenes along a zig-zag sequence of triples of edges as appear on opposite sides of each naphthalene unit. In this paper, we discuss the numbers of k-matchings and k-independent sets of double hexagonal chains, as well as Hosoya indices and Merrifield–Simmons indices, and obtain some extremal results: among all the double hexagonal chains with the same number of naphthalene units, (a) the double linear hexagonal chain has minimal k-matching number and maximal k-independent set number and (b) the double zig-zag hexagonal chain has maximal k-matching number and minimal k-independent set number, which are extensions to hexagonal chains [L. Zhang and F. Zhang, Extremal hexagonal chains concerning k-matchings and k-independent sets, J. Math. Chem. 27 (2000) 319–329].