Weak Roman domination in rooted product graphs

Abstract

In this paper, we obtain closed formulae for the weak Roman domination number of rooted product graphs. As a consequence of the study, we show that the use of rooted product graphs is a useful tool to show that the problem of computing the weak Roman domination number of a graph is NP-hard.

Keywords

• weak roman domination
• np-hard
• rooted product graphs
• corona product graphs
• protection of graphs