Jacob, Bonnie C., et al. "When "wellness" meets zero forcing." 56th Southeastern International Conference on Combinatorics, Graph Theory, and Computing. Florida Atlantic University. Boca Raton, FL. 4 Mar. 2025. Conference Presentation. *
Well-covered graphs, investigated starting in the 1970s, are graphs in which all minimal
vertex covers are minimum vertex covers. Well-dominated graphs, investigated since the
1980s, are graphs in which all minimal dominating sets are minimum dominating sets. More recently, since 2020, applying the “well” idea to zero forcing parameters has begun to be investigated. We will discuss well-forced and well-failed graphs, which are graphs in which every minimal zero forcing set is a minimum zero forcing set, and every maximal zero forcing set is a maximum zero forcing set, respectively. We’ll also discuss some recent related work.