Protection of graphs with emphasis on Cartesian product graphs

Magdalena Valveny, Juan Alberto Rodriguez-Velazquez

Published 2020-08-01Version 1

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.