  In this paper, we introduce a graph structure called linear dependence graph
of a finite dimensional vector space over a finite field. Some basic properties
of the graph like connectedness, completeness, planarity, clique number,
chromatic number etc. have been studied. It is shown that two vector spaces are
isomorphic if and only if their corresponding linear dependence graphs are
isomorphic. Also adjacency spectrum, Laplacian spectrum and distance spectrum
of the linear dependence graph have been studied.
