Article ID Journal Published Year Pages File Type
4949478 Discrete Applied Mathematics 2017 8 Pages PDF
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.
Related Topics
Physical Sciences and Engineering Computer Science Computational Theory and Mathematics
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