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.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.

arXiv:2204.05034Apr 11, 20220 citations

Quantum state transfer in graphs with tails

Pierre-Antoine Bernard, Christino Tamon, Luc Vinet +1 more

arXiv:2211.14704Linear Algebra and its ApplicationsFeb 4, 20252 citations

Quantum state transfer between twins in weighted graphs

Steve Kirkland, Hermie Monterde, Sarah Plosker

arXiv:2201.02720Journal of Algebraic CombinatoricsOct 2, 20239 citations

Quantum State Transfer in Coronas

Ethan Ackelsberg, Zachary Brehm, Ada Chan +2 more

We study state transfer in quantum walks on graphs relative to the adjacency matrix. Our motivation is to understand how the addition of pendant subgraphs affect state transfer. For two graphs $G$ and $H$ , the Frucht-Harary corona product $G \circ H$ is obtained by taking $|G|$ copies of the cone $K_{1} + H$ and by identifying the conical vertices according to $G$ . Our work explores conditions under which the corona $G \circ H$ exhibits state transfer. We also describe new families of graphs with state transfer based on the corona product. Some of these constructions provide a generalization of related known results.We study state transfer in quantum walks on graphs relative to the adjacency matrix. Our motivation is to understand how the addition of pendant subgraphs affect state transfer. For two graphs $G$ and $H$, the Frucht-Harary corona product $G \circ H$ is obtained by taking $|G|$ copies of the cone $K_{1} + H$ and by identifying the conical vertices according to $G$. Our work explores conditions under which the corona $G \circ H$ exhibits state transfer. We also describe new families of graphs with state transfer based on the corona product. Some of these constructions provide a generalization of related known results.

arXiv:1605.05260The Electronic Journal of CombinatoricsMay 19, 201722 citations

COHERENT STATES ON GRAPHS

Thomas Thiemann

The Ninth Marcel Grossmann MeetingDec 1, 20022 citations

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}

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.

We study state transfer in quantum walks on graphs relative to the adjacency matrix. Our motivation is to understand how the addition of pendant subgraphs affect state transfer. For two graphs

G

and

H

, the Frucht-Harary corona product

G \circ H

is obtained by taking

|G|

copies of the cone

K_{1} + H

and by identifying the conical vertices according to

G

. Our work explores conditions under which the corona

G \circ H

exhibits state transfer. We also describe new families of graphs with state transfer based on the corona product. Some of these constructions provide a generalization of related known results.