Total 2-domination in Grid graphs

Abstract

Let G = (V, E) be a graph, a set S C V is a total k-dominating set if every vertex V has at least k neighbors in 5. The total k-domination number 7kt(G) is the minimum cardinality among all total k-dominating sets. In this paper we obtain some closed for mulas for the total 2-domination number, also called double total domination number, of some grid graphs, and an upper and a lower bound for this parameter in any grid graph. © 2019 Utilitas Mathematica Publishing Inc.. All rights reserved.