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

Unicyclic graphs and the inertia of the distance squared matrix