Abstract
The anti-forcing number of a perfect matching M of a graph G is the minimal number of edges of G not in M whose deletion results in a subgraph with a unique perfect matching M. The maximum anti-forcing number of a benzenoid system H equals the Fries number of H. Hwang et al. defined the anti-forcing polynomial of a graph as a counting polynomial for perfect matchings with the same anti-forcing number, and obtained explicit expressions of the anti-forcing polynomial of hexagonal chains and crowns. In this paper, we focus on benzenoid systems with forcing edges, and obtain a recurrence relation of their anti-forcing polynomial. Furthermore, we get an explicit expression of the anti-forcing polynomial of benzenoid parallelograms.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
