Let be a module over a commutative ring and let be the
collection of all prime submodules of . One can define a Zariski
topology on , which is analogous to that on , and
then for any non-empty set of , it is possible to
define a simple graph , called the Zariski
topology-graph. In this paper, we study the domination number of
and some connections between the graph-theoretic
properties of and algebraic properties of the module
.

Key Words: Rings and modules, Zariski topology, graph, domination number.

2010 Mathematics Subject Classification: Primary 13C13, 13C99; Secondary 05C75.

Download the paper in pdf format here.