Continuous anti-forcing spectra of cata-condensed hexagonal systems

TL;DR

This paper proves that for cata-condensed hexagonal systems, the set of anti-forcing numbers of all perfect matchings forms a continuous integer interval, revealing a fundamental structural property.

Contribution

It establishes that the anti-forcing spectrum of cata-condensed hexagonal systems is always a continuous interval, a new insight into their combinatorial structure.

Findings

Anti-forcing spectrum is a continuous integer interval.

The result applies to all cata-condensed hexagonal systems.

Provides a structural characterization of perfect matchings.

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 make $M$ as a unique perfect matching of the resulting graph. The anti-forcing spectrum of $G$ is the set of anti-forcing numbers of 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 an integer interval.