arXiv subjects

Kellon Sandall

Publications and source records attributed to Kellon Sandall.

2 recordsLinked to original sources

arXiv2026

Pretty good quantum state transfer via transcendental edge weights

We prove that if we take a rooted product of a circulant graph with universal perfect state transfer with a path of fixed length whose end edge is weighted with a transcendental number, then there is pretty good state transfer between any pair of endpoints of these paths. As a consequence, in a path with an even number of vertices with transcendental weights on the two edges incident to the endpoints, there is pretty good state transfer.

quant-ph↗

arXiv2022

Unicyclic graphs and the inertia of the distance squared matrix

A result of Bapat and Sivasubramanian gives the inertia of the distance squared matrix of a tree. We develop general tools on how pendant vertices and degree 2 vertices affect the inertia of the distance squared 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.

math.CO↗