Abstract
A forcing set of a perfect matching M of a graph G is a subset of M contained in no other perfect matchings of G. A global forcing set of G, introduced by Vukičević et al., is a subset of E(G) on which there are distinct restrictions of any two different perfect matchings of G. Combining the above“forcing” and “global” ideas, Xu et al. [Journal of Combinatorial Optimization 29, no. 4 (2015): 803–14] introduced a complete forcing set of G defined as a subset of E(G) on which the restriction of any perfect matching M of G is a forcing set of M. The minimum cardinality of complete forcing set is the complete forcing number of G. In this paper, we give the explicit expressions for the complete forcing numbers of several classes of spiro hexagonal systems. Moreover, we also discuss some propositions of spiro cata-condensed hexagonal system with perfect matching related to the concept of forcing numbers.
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