Connected power domination number of product graphs

Abstract

In this paper, we consider the connected power domination number (γP,c) of three standard graph products. The exact value for γP,c(G•H) is obtained for any two non-trivial graphs G and H. Further, tight upper bounds are proved for the connected power domination number of the Cartesian product of two graphs G and H. Consequently, the exact value of the connected power domination number of the Cartesian product of some standard graphs is determined. Finally, the connected power domination number of tensor product of graphs is discussed.