Large sets of strongly cospectral vertices in Cayley graphs

TL;DR

This paper constructs families of abelian Cayley graphs with arbitrarily large sets of mutually strongly cospectral vertices, advancing understanding of quantum state transfer in graph structures.

Contribution

It introduces new constructions of abelian Cayley graphs featuring large sets of strongly cospectral vertices, a novel development in quantum graph theory.

Findings

Large sets of mutually strongly cospectral vertices are possible in abelian Cayley graphs.

The constructions demonstrate the potential for complex quantum state transfer networks.

The results expand the class of graphs known to support quantum information processes.

Abstract

Strong cospectrality is an equivalence relation on the set of vertices of a graph that is of importance in the study of quantum state transfer in graphs. We construct families of abelian Cayley graphs in which the number of mutually strongly cospectral vertices can be arbitrarily large.