Protection of Graphs with Emphasis on Cartesian Product Graphs

Abstract

 In this paper, we study the weak Roman domination number and the secure domination number of a graph. In particular, we obtain general bounds on these two parameters and, as a consequence of the study, we derive new inequalities of Nordhaus-Gaddum type involving secure domination and weak Roman domination.
Furthermore, the particular case of Cartesian product graphs is considered.