Non-Zero Component Graph of a Finite Dimensional Vector Space

Angsuman Das

Published 2015-06-16Version 1

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 study the automorphism group of the graph, and determine the order of the automorphism group and degree of each vertex in case the base field is finite.