Anti-forcing polynomials for benzenoid systems with forcing edges

作者：Zhao, Shuang; Zhang, Heping^*

来源：Discrete Applied Mathematics, 2018, 250: 342-356.

DOI：10.1016/j.dam.2018.05.023

• Perfect matching
• Anti-forcing number
• Anti-forcing polynomial
• Benzenoid system
• Forcing edge

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.

• 出版日期2018-12-11
• 单位兰州大学