Wenhao Zhen

activity

20232026

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Showing 2024 · math.SPShow all

4 papers · 2 filters

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…

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

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 $d$