Beschreibung:
<jats:p xml:lang="en">Let $M$ be a module over a commutative ring $R$. The
annihilating-submodule graph of $M$, denoted by $AG(M)$, is a
simple undirected graph in which a non-zero submodule $N$ of $M$
is a vertex if and only if there exists a non-zero proper
submodule $K$ of $M$ such that $NK=(0)$, where $NK$, the product
of $N$ and $K$, is denoted by $(N:M)(K:M)M$ and two distinct
vertices $N$ and $K$ are adjacent if and only if $NK=(0)$. This
graph is a submodule version of the annihilating-ideal graph and
under some conditions, is isomorphic with an induced subgraph of
the Zariski topology-graph $G(\tau_T)$ which was introduced in [H.
Ansari-Toroghy and S. Habibi, Comm. Algebra, 42(2014), 3283-3296].
In this paper, we study the domination number of $AG(M)$ and some
connections between the graph-theoretic properties of $AG(M)$ and
algebraic properties of module $M$.</jats:p>