Total Domination in Generalized $\theta$-Graphs and Ladder Graphs

Abstract

A set of vertices in a graph $G$ without isolated vertices is a total dominating set (TDS) of $G$ if every vertex of $G$ is adjacent to some vertex in $S$. The minimum cardinality of a TDS of $G$ is the total domination number ${\gamma }_t(G)$ of $G$. In this paper, the total domination number of generalized $n$-graphs and $m\times n$ ladder graphs is determined.