Global Forcing Numbers of Handgun-shaped Benzenoid Systems
Xiu-Song Liu, Shou-Jun Xu and Liangping Tu
Affiliation: School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, China.
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,
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