  The upper and lower Nordhaus-Gaddum bounds over all graphs for the power
domination number follow from known bounds on the domination number and
examples. In this note we improve the upper sum bound for the power domination
number substantially for graphs having the property that both the graph and its
complement must be connected. For these graphs, our bound is tight and is also
significantly better than the corresponding bound for domination number. We
also improve the product upper bound for the power domination number for graphs
with certain properties.
