engleski

The global forcing number of the parallelogram polyhex

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 (m ≤ n) 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.

Global forcing set; Global forcing number; Parallelogram polyhex

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