Perfect state transfer in neighborhood coronas

TL;DR

This paper investigates perfect and pretty good quantum state transfer in neighborhood corona graphs, establishing necessary conditions and identifying new graph families with these properties based on adjacency matrix analysis.

Contribution

It introduces necessary conditions for perfect state transfer in neighborhood coronas and constructs new graph families exhibiting pretty good state transfer.

Findings

Necessary conditions for perfect state transfer in neighborhood coronas.

Identification of new graph families with pretty good state transfer.

Analysis based on adjacency matrix properties.

Abstract

The neighborhood corona $G \star H$ is the graph obtained by taking one copy $G$ and $|G|$ copies of $H$, and joining each vertex of the $j$th copy of $H$ to all neighbors of $v_{j}$ in $G$. In this paper, we study the state transfer of neighborhood coronas related to the adjacency matrix. Concretely, we provide some necessary conditions under which the neighborhood corona $G \star H$ admits perfect state transfer, and obtain a new family of graphs with pretty good state transfer based on neighborhood coronas.