Power domination in certain chemical structures
Let G(V,E) G ( V , E ) be a simple connected graph. A set S?V S ? V is a power dominating set (PDS) of G, if every vertex and every edge in the system is observed following the observation rules of power system monitoring. The minimum cardinality of a PDS of a graph G  is the power domination number ?p(G) ? p ( G ) . In this paper, we establish a fundamental result that would provide a lower bound for the power domination number of a graph. Further, we solve the power domination problem in polyphenylene dendrimers, Rhenium Trioxide (ReO3) lattices and silicate networks.
power domination polyphenylene dendrimers silicate networks reo3 lattices