  In this paper, we introduce a graph structure, called non-zero component
graph on finite dimensional vector spaces. We show that the graph is connected
and find its domination number and independence number. We also study the
inter-relationship between vector space isomorphisms and graph isomorphisms and
it is shown that two graphs are isomorphic if and only if the corresponding
vector spaces are so. Finally, we determine the degree of each vertex in case
the base field is finite.
