Signless Laplacian State Transfer on Vertex Complemented Coronae

TL;DR

This paper investigates conditions for perfect and pretty good quantum state transfer on vertex complemented corona graphs using the signless Laplacian matrix, expanding understanding of quantum communication in complex graph structures.

Contribution

It introduces new conditions for signless Laplacian perfect and pretty good state transfer specifically on vertex complemented corona graphs.

Findings

Identifies conditions for perfect state transfer.

Provides mild conditions for pretty good state transfer.

Analyzes quantum state transfer properties in complex graph structures.

Abstract

Given a graph $G$ with vertex set $V(G)=\{v_1,v_2,\ldots,v_{n_1}\}$ and a graph $H$ of order $n_2$, the vertex complemented corona, denoted by $G\tilde{\circ}{H}$, is the graph produced by copying $H$ $n_1$ times, with the $i$-th copy of $H$ corresponding to the vertex $v_i$, and then adding edges between any vertex in $V(G)\setminus\{v_{i}\}$ and any vertex of the $i$-th copy of $H$. The present article deals with quantum state transfer of vertex complemented coronae concerning signless Laplacian matrix. Our research investigates conditions in which signless Laplacian perfect state transfer exists or not on vertex complemented coronae. Additionally, we also provide some mild conditions for the class of graphs under consideration that allow signless Laplacian pretty good state transfer.