Fractional revival on semi-Cayley graphs over abelian groups

TL;DR

This paper explores the conditions under which semi-Cayley graphs over finite abelian groups exhibit fractional revival, providing necessary and sufficient criteria, and illustrating applications with specific group examples.

Contribution

It establishes new necessary and sufficient conditions for fractional revival in semi-Cayley graphs over abelian groups, including integrality constraints and timing characterization.

Findings

Fractional revival occurs under specific algebraic conditions.

Integrality is necessary for fractional revival in certain semi-Cayley graphs.

Examples include Cayley graphs over dihedral and dicyclic groups exhibiting fractional revival.

Abstract

In this paper, we investigate the existence of fractional revival on semi-Cayley graphs over finite abelian groups. We give some necessary and sufficient conditions for semi-Cayley graphs over finite abelian groups admitting fractional revival. We also show that integrality is necessary for some semi-Cayley graphs admitting fractional revival. Moreover, we characterize the minimum time when semi-Cayley graphs admit fractional revival. As applications, we give examples of certain Cayley graphs over the generalized dihedral groups and generalized dicyclic groups admitting fractional revival.