Unicyclic graphs and the inertia of the squared distance matrix

Abstract

A result of Bapat and Sivasubramanian gives the inertia of the squared distance matrix of a tree. We develop general tools on how pendant vertices and vertices of degree 2 affect the inertia of the squared distance matrix and use these to give an alternative proof of this result. We further use these tools to extend this result to certain families of unicyclic graphs, and we explore how far these results can be extended.