A short note on a short remark of Graham and Lov\'{a}sz
Combinatorics
2013-10-01 v2
Abstract
Let D be the distance matrix of a connected graph G and let nn(G), np(G) be the number of strictly negative and positive eigenvalues of D respectively. It was remarked in [1] that it is not known whether there is a graph for which np(G) > nn (G). In this note we show that there exists an infinite number of graphs satisfying the stated inequality, namely the conference graphs of order> 9. A large representative of this class being the Paley graphs.The result is obtained by derving the eigenvalues of the distance matrix of a strongly-regular graph.
Keywords
Cite
@article{arxiv.1303.4517,
title = {A short note on a short remark of Graham and Lov\'{a}sz},
author = {Jernej Azarija},
journal= {arXiv preprint arXiv:1303.4517},
year = {2013}
}
Comments
5 pages, 3 figures