Dein Wong

activity

20242026

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5 papers · 1 filter

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.SP2024

Line graphs with the largest eigenvalue multiplicity

Wenhao Zhen, Dein Wong, Songnian Xu

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

math.SP2024

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

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…

Graphs with maximal Laplacian eigenvalue multiplicity

The multiplicity of the laplacian eigenvalue 1 of a tree

Line graphs with the largest eigenvalue multiplicity

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

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

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

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