On Singleton 3-Rainbow Domination of Cylindrical Graphs

Abstract

Domination is among the most popular topics in graph theory, both due to its combinatorial appeal and a number of practical applications. Cylindrical graphs are Cartesian products of a path and a cycle. Usually, for some special subfamilies, natural constructions exist that give exact solutions. On the other hand, in general, exact values of invariants on cylindrical graphs are hard to compute. In this paper, tight lower and upper bounds for singleton three-rainbow domination are proven and a subfamily of cylindrical graphs is found for which exact values are provided. The results complement recent findings for singleton two- and four-rainbow domination.