Songnian Xu

activity

20242026

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(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.GR2026

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.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 $I^$ over $G$ is a digraph that admits a group of automorphisms isomorphic to $G$ acting semiregularly o…