For a graph $G=(V,E)$, we call a subset $ S\subseteq V \cup E$ a total mixed dominating set of $G$ if each element of $V \cup E$ is either adjacent or incident to an element of $S$, and the total mixed domination number $\gamma_{tm}(G)$ of $G$ is defined as the minimum cardinality of a total mixed dominating set. In this paper, we present some tight lower and upper bounds for the total mixed domination number of a connected graph in terms of some parameters such as the order and the total domination numbers of the graph and its line graph. Also we discuse on the relation between total mixed domination number of a graph with its diameter and total domination number of the total of the graph. Then we calculate the total mixed domination number of some known graphs.
