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

Authors:
Haizhen Ren;Fuji Zhang
Affiliations:
Department of Mathematics, Qinghai Normal University, Xining, Qinghai 810008, PR China;School of Mathematical Sciences, Xiamen University, Xiamen, Fujian 361005, PR China
Venue:
Discrete Applied Mathematics
Year:
2007

Citing 2
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Maxima and Minima of the Hosoya Index and the Merrifield-Simmons Index

Acta Applicandae Mathematicae: an international survey journal on applying mathematics and mathematical applications

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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].