Physical Sciences and Mathematics Commons^™

Finding Patterns In The Inertia Of The Distance Squared Matrix Of Unicyclic Graphs, Kellon Sandall, Mark Kempton, Christian Howell

Undergraduate Honors Theses

We analyze the spectrum of the distance squared matrix of a tree and give a relation between the inertia of the distance squared matrix and the structure of the tree. We take the result one step further and consider the addition of exactly one cycle in the tree. We obtain an expression for the inertia of the distance squared matrix of a cycle graph. We obtain a bound on the inertia of the distance squared matrix of an arbitrary unicyclic graph.