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Grundy dominating sequences and zero forcing sets
In a graph a sequence of vertices is Grundy
dominating if for all we have and is Grundy total dominating if for all
we have .
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 or
. 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
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