1. Complete forcing numbers of hexagonal systems II.
- Author
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He, Xin and Zhang, Heping
- Subjects
- *
NUMBER systems , *SUBGRAPHS , *PARALLELOGRAMS , *CHARTS, diagrams, etc. , *MATHEMATICS , *BIPARTITE graphs - Abstract
The complete forcing number of a graph G is the cardinality of a minimum subset of E(G) to which the restriction of every perfect matching M is a forcing set of M. In a previous paper (He et al., J Math Chem 59:1767–1784, 2021), we presented a complete forcing set of a hexagonal system in terms of elementary edge-cut cover, and a lower bound for the complete forcing number of a normal hexagonal system by matching numbers of some subgraphs of its inner dual graph. In this paper, we show that the complete forcing number of a normal hexagonal system without 2 × 3 subsystems attains the above lower bound. As an example, we present an expression of the complete forcing numbers of pyrene systems. Besides, for a parallelogram hexagonal system, we obtain that its complete forcing number is larger than the lower bound by at most 1. [ABSTRACT FROM AUTHOR]
- Published
- 2022
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