arXiv subjects

Xing-Kun Song

Publications and source records attributed to Xing-Kun Song.

3 recordsLinked to original sources

arXiv2022

State transfer on integral mixed circulant graphs

A mixed circulant graph is called integral if all eigenvalues of its Hermitian adjacency matrix are integers. The main purpose of this paper is to investigate the existence of perfect state transfer (PST for short) and multiple state transfer (MST for short) on integral mixed circulant graphs. Concretely, we provide sufficient and necessary conditions for the existence of PST and MST between specified pairs of vertices on integral mixed circulant graphs, respectively.

math.CO↗

arXiv2022

Quantum state transfer on integral oriented circulant graphs

An oriented circulant graph is called integral if all eigenvalues of its Hermitian adjacency matrix are integers. The main purpose of this paper is to investigate the existence of perfect state transfer ($\PST$ for short) and multiple state transfer ($\MST$ for short) on integral oriented circulant graphs. Specifically, a characterization of $\PST$ (or $\MST$) on integral oriented circulant graphs is provided. As an application, we also obtain a closed-form expression for the number of integral oriented circulant graphs with fixed order having $\PST$ (or $\MST$).

math.CO↗

arXiv2022

Perfect state transfer in 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.

math.CO↗