Songnian Xu

activity

20242026

collaborators

10 papers

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

$m$ -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…

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

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

$m$ -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