Pretty good plus state transfer in cycles

TL;DR

This paper studies fractional revival and pretty good state transfer in graphs, especially cycles and their complements, revealing conditions under which these phenomena occur and extending results to weighted paths with potential.

Contribution

It provides a complete characterization of pretty good plus state transfer in cycles and their complements, and links fractional revival to graph complementation and double covers.

Findings

Fractional revival is preserved under graph complementation under certain conditions.

Complete characterization of pretty good plus state transfer in cycles and their complements.

Extension of results to weighted paths with potential.

Abstract

We investigate fractional revival in graphs with respect to the adjacency, Laplacian, and signless Laplacian matrices. We observe that, under certain conditions, fractional revival is preserved under graph complementation. Then we establish a connection between fractional revival in a graph and in its double cover, and obtain a complete characterization of pretty good plus state transfer in cycles and their complements. This leads to characterizations of pretty good vertex state transfer in weighted paths with potential.