Abstract
In this paper, we introduce and do an initial investigation of a variant of Grundy hop domination in a graph called the connected Grundy hop domination. We show that the connected Grundy hop domination number lies between the connected hop domination and Grundy hop domination number of a graph. In particular, we give realization results involving connected hop domination, connected Grundy hop domination, and Grundy hop domination numbers. Moreover, we determine the connected Grundy hop domination numbers of some graphs.
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