Abstract
Let G be a molecular graph with bond set E(G) that admits a Kekulé structure. A global forcing set of G is any subset of E(G) such that no two Kekulé structures of G coincide on S. The number of bonds in a global forcing set of the smallest cardinality is called the global forcing number of G. The global forcing number gives some sort of identification of the minimal amount of information required to specify Kekule structures of a molecular graph. In this article, we give explicit formulae for global forcing numbers of handgun-shaped benzenoid systems. As a corollary, formulae for the global forcing numbers of parallelogram benzenoid systems can be obtained. [J. Sedlar, The global forcing number of the parallelogram polyhex, Discrete Appl. Math. 160 (2012) 2306-2313].
Keywords: Benzenoid hydrocarbon, global forcing number, global forcing set, handgun-shaped benzenoid system, Kekule structure, perfect matching.
Current Nanoscience
Title:Global Forcing Numbers of Handgun-shaped Benzenoid Systems
Volume: 10 Issue: 5
Author(s): Xiu-Song Liu, Shou-Jun Xu and Liangping Tu
Affiliation:
Keywords: Benzenoid hydrocarbon, global forcing number, global forcing set, handgun-shaped benzenoid system, Kekule structure, perfect matching.
Abstract: Let G be a molecular graph with bond set E(G) that admits a Kekulé structure. A global forcing set of G is any subset of E(G) such that no two Kekulé structures of G coincide on S. The number of bonds in a global forcing set of the smallest cardinality is called the global forcing number of G. The global forcing number gives some sort of identification of the minimal amount of information required to specify Kekule structures of a molecular graph. In this article, we give explicit formulae for global forcing numbers of handgun-shaped benzenoid systems. As a corollary, formulae for the global forcing numbers of parallelogram benzenoid systems can be obtained. [J. Sedlar, The global forcing number of the parallelogram polyhex, Discrete Appl. Math. 160 (2012) 2306-2313].
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Cite this article as:
Liu Xiu-Song, Xu Shou-Jun and Tu Liangping, Global Forcing Numbers of Handgun-shaped Benzenoid Systems, Current Nanoscience 2014; 10 (5) . https://dx.doi.org/10.2174/1573413710666140422231509
DOI https://dx.doi.org/10.2174/1573413710666140422231509 |
Print ISSN 1573-4137 |
Publisher Name Bentham Science Publisher |
Online ISSN 1875-6786 |
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