A note on sub-total domination in graphs

Let $G$ be a simple and finite graph without isolated vertices. In this paper we introduce and study a new degree sequence derived invariant called the \emph{sub-total domination number}, denoted ${\subset }_t(G)$. In particular, we show that ${\subset }_t(G)$ serves as a lower bound on ${\gamma }_t(G)$, where ${\gamma }_t(G)$ denotes the heavily studied \emph{total domination number} of $G$.