Wenhao Zhen

activity

20232026

collaborators

10 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(λ) $ denotes the multiplicity of $ λ$ as an eigenvalue of the Laplacian matrix $ L(G) $. Let $ p(G) $ denote t…

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 $m_{G} (λ)$ be the multiplicity of an eigenvalue $λ$ of $L (G)$ . When $G$ is a…

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.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.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.SP2024

Line graphs with the largest eigenvalue multiplicity

Wenhao Zhen, Dein Wong, Songnian Xu

For a connected graph $G$ , we denote by $L (G)$ , $m_{G} (λ)$ , $c (G)$ and $p (G)$ the line graph of $G$ , the eigenvalue multiplicity of $λ$ in $G$ , the cyclomatic number and the number…

math.SP2024

A characterization of graphs $G$ with $m_{G} (λ) = 2 c (G) + q_{s} (G) - 1$

Songnian Xu, Wenhao Zhen, Dein Wong

Let $G$ be a simple connected graph. If every pendant path in $G$ is at least $P_{s}$ , we denote that $G \in G_{s}$ . For $G \in G_{s}$ , let $Q_{s} (G)$ be the set of vertic…

math.SP2024

A complete characterization of graphs for which $m_{G} (- 1) = n - d - 1$

Songnian Xu, Wenhao Zhen, Dein Wong

Let $G$ be a simple connected graph of order $n$ with diameter $d$ . Let $m_{G} (- 1)$ denote the multiplicity of the eigenvalue $- 1$ of the adjacency matrix of $G$ , and let $P = P_{d+1…

math.SP2024

The relationship between the negative inertia index of graph $G$ and its girth $g$ and diameter $d$

Songnian Xu, Wenhao Zhen, Dein Wong

Let $G$ be a simple connected graph. We use $n (G)$ , $p (G)$ , and $η (G)$ to denote the number of negative eigenvalues, positive eigenvalues, and zero eigenvalues of the adjacency mat…

math.SP2023

Minimal graphs with eigenvalue multiplicity of $n - d$

Yuanshuai Zhang, Dein Wong, Wenhao Zhen

For a connected graph $G$ with order $n$ , let $e (G)$ be the number of its distinct eigenvalues and $d$ be the diameter. We denote by $m_{G} (μ)$ the eigenvalue multiplicity of $μ$ in…

Graphs with maximal Laplacian eigenvalue multiplicity

The multiplicity of the laplacian eigenvalue 1 of a tree

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

Laplacian eigenvalue distribution and girth of graphs

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

Line graphs with the largest eigenvalue multiplicity

A characterization of graphs G with mG​(λ)=2c(G)+qs​(G)−1

A complete characterization of graphs for which mG​(−1)=n−d−1

The relationship between the negative inertia index of graph G and its girth g and diameter d

Minimal graphs with eigenvalue multiplicity of n−d

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

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

A characterization of graphs $G$ with $m_{G} (λ) = 2 c (G) + q_{s} (G) - 1$

A complete characterization of graphs for which $m_{G} (- 1) = n - d - 1$

The relationship between the negative inertia index of graph $G$ and its girth $g$ and diameter $d$

Minimal graphs with eigenvalue multiplicity of $n - d$