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The maximum forcing number of cylindrical grid, toroidal 4-8 lattice and Klein bottle 4-8 lattice

机译：The maximum forcing number of cylindrical grid, toroidal 4-8 lattice and Klein bottle 4-8 lattice

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摘要

Let G be a graph that admits a perfect matching. A forcing set for a perfect matching M of G is a subset S of M, such that S is contained in no other perfect matchings of G. The smallest cardinality of a forcing set of M is called forced matching number, denoted by f (G, M). Among all perfect matchings of G, the maximum forcing matching number is called the maximum forcing number of G, denoted by F(G). In this paper, we show that the maximum forcing numbers of cylindrical grid P-2m x C2n+1 is m(n + 1) by choosing a suitable independent set of this graph. This solves an open problem proposed by Afshani et al. (Australas J Combin 30: 147-160, 2004). Moreover, we obtain that the maximum forcing numbers of two classes of toroidal 4-8 lattice and two classes of Klein bottle 4-8 lattice are all equal to the number of squares pq.

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