Given a simple graph G, let Z(G),p(G),Φ(G),ex(G) and M(G), respectively, be the zero forcing number, the number of pendant vertices, the cyclomatic number, the number of exterior major vertices and the maximum nullity of G. Wang et al. (Linear Multilinear Algebra, 2018. https://doi.org/10.1080/03081087.2018.1545829) established upper and lower bounds on Z(G) with respect to p(G),ex(G) and Φ (G) : p(G) - ex(G) - 1 ⩽ Z(G) ⩽ p(G) + 2 Φ (G) + 1. Hence, it is interesting to study the distribution of the zero forcing number Z(G) in the interval ...
