We define the anti-forcing number of a perfect matching M of a graph G as the minimal
number of edges of G whose deletion results in a subgraph with a unique perfect matching …

The notions of a forcing edge and the forcing number of a perfect matching first appeared in
a 1991 paper [15] by Harary, Klein and Zivkovic. The root of these concepts can be traced to …

The forcing number or the degree of freedom of a perfect matching M of a graph G is the
cardinality of the smallest subset of M that is contained in no other perfect matchings of G. In …

Let G be a graph that admits a perfect matching M. A forcing set S for a perfect matching M is
a subset of M such that it is contained in no other perfect matchings of G. The cardinality of a …

Klein and Randic defined the innate degree of freedom of a graph G as the sum of the
forcing numbers (innate degree of freedom) of perfect matchings of graph G. In this paper …

Let M be a perfect matching of a graph G. The smallest number of edges whose removal to
make M as the unique perfect matching in the resulting subgraph is called the anti-forcing …

The forcing polynomial and anti-forcing polynomial are two important enumerative
polynomials associated with all perfect matchings of a graph. In a graph with large order, the …

The forcing number of a perfect matching M of a graph G is the minimal number of edges of
M that are contained in no other perfect matchings of G. The anti-forcing number of M in G is …

The forcing number of a perfect matching of a graph was introduced by Harary et al., which
originated from Klein and Randi\'{c}'s ideal of innate degree of freedom of Kekul\'{e} structure …

Let G be a graph that admits a perfect matching M. A forcing set S for a perfect matching M is
a subset of M such that it is contained in no other perfect matchings of G. The smallest …