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Published in:
01-07-2016
Complete forcing numbers of primitive coronoids
Published in: Journal of Combinatorial Optimization | Issue 1/2016
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Abstract
Let \(G\) be a graph with edge set \(E(G)\) that admits a perfect matching \(M\). A forcing set of \(M\) is a subset of \(M\) contained in no other perfect matching of \(G\). A complete forcing set of \(G\), recently introduced by Xu et al. (J Combin Optim 29(4):803–814, 2015c), is a subset of \(E(G)\) to which the restriction of any perfect matching is a forcing set of the perfect matching. The minimum possible cardinality of a complete forcing set of \(G\) is the complete forcing number of \(G\). Previously, Xu et al. (J Combin Optim 29(4):803–814, 2015c) gave an expression for the complete forcing number of a hexagonal chain and a recurrence relation for complete forcing numbers of catacondensed hexagonal systems. In this article, by the constructive proof, we give an explicit analytical expression for the complete forcing number of a primitive coronoid, a circular single chain consisting of congruent regular hexagons (i.e., Theorem 3.9).