Document Type

Journal Article

Department/Unit

Department of Mathematics

Abstract

Applying the recently obtained distributive lattice structure on the set of 1-factors, we show that the resonance graphs of any benzenoid systems G, as well as of general plane (weakly) elementary bipartite graphs, are median graphs and thus extend greatly Klavžar et al.'s result. The n-dimensional vectors of nonnegative integers as a labelling for the 1-factors of G with n inner faces are described. The labelling preserves the partial ordering of the above-mentioned lattice and can be transformed into a binary coding for the 1-factors. A simple criterion for such a labelling being binary is given. In particular, Klavžar et al.'s algorithm is modified to generate this binary coding for the 1-factors of a cata-condensed benzenoid system.

Publication Year

2008

Journal Title

SIAM Journal on Discrete Mathematics

Volume number

22

Issue number

3

Publisher

Society for Industrial and Applied Mathematics

First Page (page number)

971

Last Page (page number)

984

Referreed

1

DOI

10.1137/070699287

ISSN (print)

08954801

Keywords

1-factor, benzenoid system, distributive lattice, resonance graph, Z-transformation graph, binary coding, median graph

Included in

Mathematics Commons

Share

COinS