arXiv:2202.07202

Laplacian state transfer in vertex complemented coronas

Qiang Wang, Xiaogang Liu

Published Feb 15, 2022• 0 citations

Abstract

In this paper, we investigate the existence of Laplacian perfect state transfer and Laplacian pretty good state transfer in vertex complemented coronas. We prove that there is no Laplacian perfect state transfer in vertex complemented coronas. In contrast, we give a sufficient condition for vertex complemented coronas to have Laplacian pretty good state transfer.

DOI: 10.48550/arxiv.2202.07202

Related papers

Laplacian state transfer in edge coronas

Yipeng Li, Xiaogang Liu, Shenggui Zhang

Linear and Multilinear AlgebraApr 7, 20208 citations

Signless Laplacian State Transfer on Vertex Complemented Coronae

Zhu, Ke-Yu, Gui‐Xian Tian, Shu‐Yu Cui

arXiv:2502.14460Feb 20, 20250 citations

Perfect state transfer in neighborhood coronas

Xing-Kun Song

arXiv:2204.05034Apr 11, 20220 citations

Pretty good plus state transfer in cycles

Sarojini Mohapatra, Hiranmoy Pal

math.COCross-listedarXiv:2603.17595Mar 19, 2026

Constructing graphs having Laplacian pair state transfer by an edge perturbation

Wei Wang, Xiaogang Liu, Jing Wang

In this paper, we give some sufficient conditions for graphs with an edge perturbation between twin vertices to have Laplacian perfect pair state transfer as well as Laplacian pretty good pair state transfer. By those sufficient conditions, we also construct many new graphs having Laplacian perfect pair state transfer as well as Laplacian pretty good pair state transfer.

arXiv:2202.04957Feb 10, 20220 citations

Laplacian pretty good edge state transfer in paths

Wang, Wei, Xiaogang Liu, Jing Wang

In this paper, we first give a necessary and sufficient condition for a graph to have Laplacian pretty good pair state transfer. As an application of such result, we give a complete characterization of Laplacian pretty good edge state transfer in paths.

arXiv:2209.04630Sep 10, 20220 citations

arXiv:2202.07202

Laplacian state transfer in vertex complemented coronas

Qiang Wang, Xiaogang Liu

Published Feb 15, 2022• 0 citations

arXiv HTML PDF

Abstract

DOI: 10.48550/arxiv.2202.07202

Related papers

Laplacian state transfer in edge coronas

Yipeng Li, Xiaogang Liu, Shenggui Zhang

Characterizing which graphs have Laplaican perfect state transfer or Laplacian pretty good state transfer is an interesting and desirable problem. In this paper, we investigate the existence of Laplacian perfect state transfer and Laplacian pretty good state transfer in edge coronas. We give sufficient conditions for edge coronas to not have Laplacian perfect state transfer as well as sufficient conditions for edge coronas to have Laplacian perfect state transfer. Additionally, we also give sufficient conditions for edge coronas to have Laplacian pretty good state transfer.Characterizing which graphs have Laplaican perfect state transfer or Laplacian pretty good state transfer is an interesting and desirable problem. In this paper, we investigate the existence of Laplacian perfect state transfer and Laplacian pretty good state transfer in edge coronas. We give sufficient conditions for edge coronas to not have Laplacian perfect state transfer as well as sufficient conditions for edge coronas to have Laplacian perfect state transfer. Additionally, we also give sufficient conditions for edge coronas to have Laplacian pretty good state transfer.

Linear and Multilinear AlgebraApr 7, 20208 citations

Signless Laplacian State Transfer on Vertex Complemented Coronae

Zhu, Ke-Yu, Gui‐Xian Tian, Shu‐Yu Cui

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.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.

arXiv:2502.14460Feb 20, 20250 citations

Perfect state transfer in neighborhood coronas

Xing-Kun Song

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

Pretty good plus state transfer in cycles

Sarojini Mohapatra, Hiranmoy Pal

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.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.

math.COCross-listedarXiv:2603.17595Mar 19, 2026

Constructing graphs having Laplacian pair state transfer by an edge perturbation

Wei Wang, Xiaogang Liu, Jing Wang

arXiv:2202.04957Feb 10, 20220 citations

Laplacian pretty good edge state transfer in paths

Wang, Wei, Xiaogang Liu, Jing Wang

arXiv:2209.04630Sep 10, 20220 citations

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.

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.