Zhengbo Chen

collaborators

6 papers

math.CO2026

A sharp bound for the least signless Laplacian eigenvalue of triangle-free graphs

Dongxiu Cai, Zhengbo Chen, Xiao-Dong Zhang

We prove that every finite simple triangle-free graph $G$ on $n \geq 1$ vertices satisfies $q_{m i n} (G) \leq 7 n /50$ , where $q_{m i n} (G)$ is the least eigenvalue of its signless Laplaci…

math.CO2026

On the structure of graphs with given odd girth and large algebraic connectivity

Zhengbo Chen, Chenxing Li, Zhouningxin Wang

A classical result of Andrásfai, Erdős, and Sós states that every $n$ -vertex graph with odd girth at least $2 k + 1$ and minimum degree larger than $\frac{2 n}{2 k + 1}$ is bipartite. Rat…

math.CO2026

The Sharp Upper Bounds for the Median Eigenvalues of Graphs

Zhengbo Chen, Yuzhenni Wang, Xiao-Dong Zhang

Let $λ_{1} \geq λ_{2} \geq \dots \geq λ_{n}$ be the eigenvalues of a simple graph $G$ of order $n$ . The HL-index of $G$ is defined by $R (G) = max ∥ λ_{h} ∣, ∣ λ_{ℓ} ∣}$ with $h=\lfloor(n+1)/2\rfloo…

math.CO2026

The Equality Cases For the Laplacian Conjecture of Brouwer

Dongxiu Cai, Zhengbo Chen, Jia Yang +1

The Laplacian conjecture of Brouwer asserts that for any graph $G$ of order n with $m$ edges, the sum of the $k$ largest Laplacian eigenvalues satisfies \(s_k(G) \le m + \bin…

math.CO2026

The Equality Cases for the Grone-Merris-Bai Theorem

Dongxiu Cai, Zhengbo Chen, Jia Yang +1

The Grone--Merris inequality, conjectured by Grone and Merris~(1994) and first proved by Bai~(2011), states that for every graph $G$ of order $n$ and every $1 \leq k \leq n$ , $\sum_{i=…

math.CO2026

Positive and negative 3-energies of graphs

Zhengbo Chen, Zhouningxin Wang, Xiao-Dong Zhang

For a simple graph $G$ with $n$ vertices, let $A_{G}$ denote the adjacency matrix of $G$ , and let $λ_{1} (G) \geq λ_{2} (G) \geq \dots \geq λ_{n} (G)$ be its eigenvalues. For an integer $p \g…