Title: Grundy dominating sequences and zero forcing sets,
Abstract: In a graph $G$ a sequence $v_1,v_2,\dots,v_m$ of vertices is Grundy
dominating if for all $2\le i \le m$ we have $N[v_i]\not\subseteq
\cup_{j=1}^{i-1}N[v_j]$ and is Grundy total dominating if for all $2\le i \le
m$ we have $N(v_i)\not\subseteq \cup_{j=1}^{i-1}N(v_j)$. The length of the
longest Grundy (total) dominating sequence has been studied by several authors.
In this paper we introduce two similar concepts when the requirement on the
neighborhoods is changed to $N(v_i)\not\subseteq \cup_{j=1}^{i-1}N[v_j]$ or
$N[v_i]\not\subseteq \cup_{j=1}^{i-1}N(v_j)$. In the former case we establish a
strong connection to the zero forcing number of a graph, while we determine the
complexity of the decision problem in the latter case. We also study the
relationships among the four concepts, and discuss their computational
complexities.