Fractional revival on Cayley graphs over abelian groups

TL;DR

This paper characterizes when Cayley graphs over finite abelian groups exhibit fractional revival, providing necessary and sufficient conditions, and applies these results to circulant and cubelike graphs.

Contribution

It offers a complete characterization of fractional revival in Cayley graphs over abelian groups, including specific classes like circulant and cubelike graphs.

Findings

Necessary and sufficient conditions for fractional revival

Characterization of fractional revival in circulant graphs

Characterization of fractional revival in cubelike graphs

Abstract

In this paper, we investigate the existence of fractional revival on Cayley graphs over finite abelian groups. We give a necessary and sufficient condition for Cayley graphs over finite abelian groups to have fractional revival. As applications, the existence of fractional revival on circulant graphs and cubelike graphs are characterized.