Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4949478 | Discrete Applied Mathematics | 2017 | 8 Pages |
Abstract
Let G be a (4,6)-fullerene graph. We show that the maximum forcing number of G is equal to its Clar number, and the maximum anti-forcing number of G is equal to its Fries number, which extend the known results for hexagonal systems with a perfect matching (Xu et al., 2013; Lei et al., 2016). Moreover, we obtain two formulas dependent only on the order of G to count the Clar number and Fries number of G respectively. Hence we can compute the maximum forcing number of a (4,6)-fullerene graph in linear time. This answers an open problem proposed by Afshani et al. (2004) in the case of (4,6)-fullerene graphs.
Keywords
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Lingjuan Shi, Hongwei Wang, Heping Zhang,