Wenhao Zhen

activity

20242026

collaborators

8 papers

math.SP2026

Graphs with maximal Laplacian eigenvalue multiplicity

Songnian Xu, Xiaoya Li, Dein Wong +1

In this paper, $ G $ is a simple connected graph, and $ m_G(Î») $ denotes the multiplicity of $ Î»$ as an eigenvalue of the Laplacian matrix $ L(G) $. Let $ p(G) $ denote…

math.SP2026

The multiplicity of the laplacian eigenvalue 1 of a tree

Songnian Xu, Dein Wong, Wenhao Zhen

Let $G$ be a connected, undirected simple graph. Denote by $L (G)$ the Laplacian matrix of $G$ , and let $m_{G} (I^»)$ be the multiplicity of an eigenvalue $I^»$ of $L (G)$ . When $G$ is…

math.GR2025

$m$ -partite oriented semiregular representation of valency 3 for finite groups

Songnian Xu, Dein Wong, Wenhao Zhen

Let $G$ be a finite group and $m \geq 2$ a positive integer. We say that $G$ admits an \emph{oriented $m$ -semiregular representation} (abbreviated as OmSR) if there exists a $m$ -Ca…

math.GR2025

The $m$ -partite digraphical representations of valency 3 of finite groups generated by two elements

Songnian Xu, Dein Wong, Chi Zhang +1

Let $G$ be a finite group and $m$ be an integer. We employ the notation $g_{i}$ to represent elements $(g, i)$ in the Cartesian product $G \times Z_{m}$ , where $Z_{m}$ d…

math.CO2025

Laplacian eigenvalue distribution and girth of graphs

Wenhao Zhen, Dein Wong, Songnian Xu

Let $G$ be a connected graph on $n$ vertices with girth $g$ . Let $m_{G} I$ denote the number of Laplacian eigenvalues of graph $G$ in an interval $I$ . In this paper, we show that if $…

math.SP2024

Line graphs with the largest eigenvalue multiplicity