Copyright © 2013 Xiaoling Zhang and Chengyuan Song. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let denote the distance matrix of a connected graph . The inertia of is the triple of integers (), where , , and denote the number of positive, 0, and negative eigenvalues of , respectively. In this paper, we mainly study the inertia of distance matrices of some graphs related to wheel graphs and give a construction for graphs whose distance matrices have exactly one positive eigenvalue.