The Minimum Forcing and Anti-Forcing Numbers of Convex Hexagonal Systems
Yaxian Zhang, Heping Zhang · Lanzhou University Institutional Repository · 2021
A convex hexagonal system (CHS) is a hexagonal system whose inner dual has the convex polygonal boundary. The minimum forcing number of a graph G is the smallest cardinality of a matching of G contained in a unique perfect matching. The minimum anti-forcing number of G is the smallest cardinality of an edge subset of G whose deletion results in a graph with exactly one perfect matching. In this paper, we proved that for any convex hexagonal system H(a(1), a(2), a(3)) with a perfect matching, its minimum forcing and anti-forcing numbers are both equal to ={a(1), a(2), a(3)} by applying perfect path systems.