Protection of Lexicographic Product Graphs

Abstract

In this paper, we study the weak Roman domination number and the secure domination number of lexicographic product graphs. In particular, we show that these two parameters coincide for almost all lexicographic product graphs. Furthermore, we obtain tight bounds and closed formulas for these parameters.

Keywords

• lexicographic product
• weak roman domination
• secure domination
• total domination
• double total domination
• 05c69
• 05c76