Songnian Xu

activity

20232026

collaborators

15 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.GR2026

On automorphism group of the reduced finitary power monoid of the additive group of integers

Dein Wong, Songnian Xu, Chi Zhang +1

Let $Z$ be the additive group of all integers and $N$ the sub-monoid of $Z$ of all non-negative integers. For a finite subset $X$ of $Z$ , we den…

math.GR2025

On automorphism groups of power semigroups over numerical semigroups or over numerical monoids

Dein Wong, Songnian Xu, Chi Zhang +1

A numerical semigroup $S$ is a cofinite subsemigroup of $N$ , where $N$ is the additive monoid of non-negative integers. Denote by $P_{fin} (S)$ the…

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

On oriented $m$ -semiregular representations of finite groups about valency three

Songnian Xu, Dein Wong, Chi Zhang +1

Let $G$ be a group and $m$ a positive integer. We say an $m$ -Cayley digraph $Γ$ over $G$ is a digraph that admits a group of automorphisms isomorphic to $G$ acting semiregularly on…

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.GR2025

Finite groups admitting a regular tournament $m$ -semiregular representation

Dein Wong, Songnian Xu, Chi Zhang +1

For a positive integer $m$ , a finite group $G$ is said to admit a tournament $m$ -semiregular representation (TmSR for short) if there exists a tournament $Γ$ such that the automorp…

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 characterization of graphs $G$ with nullity $n (G) - d (G) - 1$

Songnian Xu

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

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.CO2023

Near automorphisms of $G_{(n, m)}$

Songnian Xu

Let $G$ be a graph with vertex set $V (G)$ , $f$ a permutation of $V (G)$ . Define $δ_{f} (G) = ∣ d (x, y) - d (f (x), f (y)) ∣$ and $δ_{f} (G) = Σ δ_{f} (x, y)$ , where the sum is taken over all unordered pair…

Graphs with maximal Laplacian eigenvalue multiplicity

The multiplicity of the laplacian eigenvalue 1 of a tree

On automorphism group of the reduced finitary power monoid of the additive group of integers

On automorphism groups of power semigroups over numerical semigroups or over numerical monoids

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

On oriented m-semiregular representations of finite groups about valency three

Laplacian eigenvalue distribution and girth of graphs

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

Finite groups admitting a regular tournament m-semiregular representation

Line graphs with the largest eigenvalue multiplicity

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

A characterization of graphs G with nullity n(G)−d(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

Near automorphisms of G(n,m)​

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

On oriented $m$ -semiregular representations of finite groups about valency three

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

Finite groups admitting a regular tournament $m$ -semiregular representation

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

A characterization of graphs $G$ with nullity $n (G) - d (G) - 1$

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 $d$

Near automorphisms of $G_{(n, m)}$