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.