Continuous forcing spectrum of regular hexagonal polyhexes

作者：

Highlights：

• A polyhex with a perfect matching can be viewed as as molecular graph (carbonskeleton) of a benzenoid hydrocarbon.

• Afshani et al. proved that any finite set of positive integers can be the forcing spectrum (the set of forcing numbers of all perfect matchings) of a planar bipartite graph.

• For a polyhex containing a 3-divisible perfect matching, we obtained its minimum forcing number and anti-forcing number, which extend the corresponding results in convex polyhexes.

• We proved that the forcing spectrum of any regular convex polyhex is an integer interval from the minimum forcing number to the Clar number.

摘要

•A polyhex with a perfect matching can be viewed as as molecular graph (carbonskeleton) of a benzenoid hydrocarbon.•Afshani et al. proved that any finite set of positive integers can be the forcing spectrum (the set of forcing numbers of all perfect matchings) of a planar bipartite graph.•For a polyhex containing a 3-divisible perfect matching, we obtained its minimum forcing number and anti-forcing number, which extend the corresponding results in convex polyhexes.•We proved that the forcing spectrum of any regular convex polyhex is an integer interval from the minimum forcing number to the Clar number.

论文关键词：Polyhex,Regular hexagonal polyhex,Prolate triangle polyhex,Perfect matching,Forcing number,Forcing spectrum

论文评审过程：Received 16 May 2021, Revised 28 February 2022, Accepted 2 March 2022, Available online 16 March 2022, Version of Record 16 March 2022.

论文官网地址：https://doi.org/10.1016/j.amc.2022.127058