Boyer et al.'s zero forcing set domination conjecture for paths

Let $G$ be a graph on $n$ vertices, and let $z(G;i)$ denote the number of zero forcing sets of $G$ of size $i$. Let $P_n$ be the path graph on $n$ vertices.

Boyer et al.'s conjecture. For every graph $G$ on $n$ vertices,

$$z(G;i)\leq z(P_n,i)$$

for all $i\geq 1$.

The conjecture asserts that paths dominate all graphs in the number of zero forcing sets of each positive size. It arises from the counting problem for zero forcing sets, which has been studied for several graph classes; its resolution is not indicated in the supplied text.