Matching anti-forcing polynomials of catacondensed hexagonal systems

Abstract

Lei, Yeh and Zhang put forward the anti-forcing number af(G,M) for a perfect matching M in a graph G, which is the minimum number of edges of G not in M whose deletion results in a subgraph with a unique perfect matching M. The anti-forcing numbers of all perfect matchings form the anti-forcing spectrum of G. The anti-forcing polynomial Af(G,x) of G is a counting polynomial for classifying perfect matchings possessing the same anti-forcing number in G. In this paper, we deduce recurrence formula of the anti-forcing polynomial and continuity of the anti-forcing spectrum for catacondensed hexagonal systems.