Zhengbo Chen

collaborators

4 papers

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 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

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

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 $I^»_{1} (G) \geq I^»_{2} (G) \geq \dots \geq I^»_{n} (G)$ be its eigenvalues. For an integer $p…