Let
![$M$](img4.png)
be a module over a commutative ring and let
![$Spec(M)$](img5.png)
be the
collection of all prime submodules of
![$M$](img4.png)
. One can define a Zariski
topology on
![$Spec(M)$](img5.png)
, which is analogous to that on
![$Spec(R)$](img6.png)
, and
then for any non-empty set
![$T$](img7.png)
of
![$Spec(M)$](img5.png)
, it is possible to
define a simple graph
![$G(\tau_T)$](img8.png)
, called the Zariski
topology-graph. In this paper, we study the domination number of
![$G(\tau_T)$](img8.png)
and some connections between the graph-theoretic
properties of
![$G(\tau_T)$](img8.png)
and algebraic properties of the module
![$M$](img4.png)
.