On the power domination number of the Cartesian product of graphs

Abstract

We give a brief survey about the existing results on the power domination of the Cartesian product of graphs, and improve two of the results by determining the exact power domination numbers of two families of graphs, namely, the cylinder and the tori . We also establish the power domination number for , the Cartesian product of a complete graph and a star.

Keywords

• electric power monitoring
• power domination
• zero forcing
• cartesian product