The global forcing number of the parallelogram polyhex

https://doi.org/10.1016/j.dam.2012.05.021Get rights and content
Under an Elsevier user license
open archive

Abstract

A global forcing set in a simple connected graph G with a perfect matching is any subset S of E(G) such that the restriction of the characteristic function of perfect matchings of G on S is an injection. The number of edges in a global forcing set of the smallest cardinality is called the global forcing number of G. In this paper we prove that for a parallelogram polyhex with m rows and n columns of hexagons (mn) the global forcing number equals m(n+1)/2 if m is even, and n(m+1)/2 if m is odd. Also, we provide an example of a minimum global forcing set.

Keywords

Global forcing set
Global forcing number
Parallelogram polyhex

Cited by (0)