Grundy Dominating and Grundy Hop Dominating Sequences in Graphs: Relationships and Some Structural Properties
Keywords:Grundy dominating sequence, Grundy hop dominating sequence, Grundy domination number, Grundy hop domination number
In this paper, we revisit the concepts of Grundy domination and Grundy hop domination in graphs and give some realization results involving these parameters. We show that the Grundy domination number and Grundy hop domination number of a graph G are generally incomparable (one is not always less than or equal the other). It is shown that their absolute difference can be made arbitrarily large. Moreover, the Grundy domination numbers of some graphs are determined.
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