On the spectrum of linear dependence graph of finite dimensional vector spaces
Combinatorics
2017-03-31 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1703.10460,
title = {On the spectrum of linear dependence graph of finite dimensional vector spaces},
author = {A. K. Bhuniya and Sushobhan Maity},
journal= {arXiv preprint arXiv:1703.10460},
year = {2017}
}
Comments
3 figures