Graphs with equal Total Domination and Inverse Total Domination Numbers

Abstract

Let $\mathrm{D}$ be a minimum total dominating set of $G=(V, E)$. If $V-D$ contains a total dominating set $D^{\prime}$ of $\mathrm{G}$, then $D^{\prime}$ is called an inverse total dominating set with respect to D. The inverse total domination number $\gamma_t(G)$ of $G$ is the minimum cardinality of an inverse total domination set of $\mathrm{G}$. In this paper, we obtain some graphs for which $\gamma_t(G)=\gamma_t^{-1}(G)$. Also we find some graphs for which $\gamma_t(G)=\gamma_t^{-1}(G)=\frac{p}{2}$.