Anti-forcing spectrum of any cata-condensed hexagonal system is continuous

Abstract

The anti-forcing number of a perfect matching M of a graph G is the minimal number of edges not in M whose removal makes M a unique perfect matching of the resulting graph. The anti-forcing spectrum of G is the set of anti-forcing numbers over all perfect matchings of G: In this paper, we prove that the anti-forcing spectrum of any cata-condensed hexagonal system is continuous, that is, it is a finite set of consecutive integers.

Keywords

Perfect matching / anti-forcing number / anti-forcing spectrum / hexagonal system

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2016 Higher Education Press and Springer-Verlag Berlin Heidelberg