Abstract
The power domination problem in graphs consists of finding a minimum set of vertices that monitors the entire graph G governed by two ‘monitoring rules’- domination and propagation. A set is a power dominating set (PDS) if it can monitor all vertices of G. The minimum cardinality of a PDS of G is called the power domination number, , of G. In this paper, we study the power domination problem in Mycielskian of spiders. For a spider T, we have and . We characterize spiders, T, for which and
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