  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 the minimum cardinality of a total mixed dominating
set of $G$. In this paper, we initiate to study the total mixed domination
number of a connected graph by giving some tight bounds in terms of some
parameters such as order and total domination numbers of the graph and its line
graph. Then we discuss on the relation between total mixed domination number of
a graph and its diameter. Studing of this number in trees is our next work.
Also we show that the total mixed domination number of a graph is equale to the
total domination number of a graph which is obtained by the graph. Giving the
total mixed domination numbers of some special graphs is our last work.
