Alternative extremal families for minimal zero forcing discrepancy

Determine whether infinite families of graphs other than the family presented in Proposition 2.10 satisfy md(G_n)=n-6.

Background

The paper proves that, for every graph of order n≥17, the minimal zero forcing set discrepancy md(G)=Z−Z(G) is at most n−6, and constructs an infinite family G_n=(P_2∪K_1)∨P_{n−3} attaining equality. The authors ask whether this extremal behavior is unique to that construction or occurs in other infinite graph families.