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A vertex cover of a graph $G = (V, E)$ is a set $X \subseteq V$ such thateach edge of $G$ is incident to at least one vertex of $X$. A dominating set $D\subseteq V$ is a total dominating set of $G$ if the subgraph induced by $D$has no isolated vertices. A $(\gamma_t-\tau)$-set of $G$ is a minimum vertexcover which is also a minimum total dominating set. In this article we give aconstructive characterization of trees having a $(\gamma_t-\tau)$-set.

A characterization of trees having a minimum vertex cover which is also a minimum total dominating set