Nonzero Component Graph of a Finite Dimensional Vector Space

In this article, we introduce a graph structure, called a nonzero 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.