Chen-Hui Lv

activity

20242026

collaborators

10 papers

math.CO2026

Automorphism groups of endomorphism monoids of $0$ -unit $3$ -valent circulant digraphs

Chenhui Lv

Let $G=\Cay(\mathbb{Z}_n,S)$ be a $3$ -valent circulant digraph with connection set $S = {0, s, t}$ , where $s, t \in Z_{n}^{*}$ and $t \neq = \pm s$ . Determining the automorphism group…

math.CO2026

The Aldous property for normal Cayley graphs on symmetric groups

Chenhui Lv, Sanming Zhou

Aldous' spectral gap conjecture states that the random walk and the interchange process on any connected graph have the same spectral gap, or, equivalently, the second largest eige…

math.CO2026

Amply regular graphs with $μ$ close to half the valency and group divisible designs

Wei Jin, Jack H. Koolen, Chenhui Lv

In this paper, we classify connected amply regular graphs with diameter $d \geq 4$ and parameters $(v, k, λ, μ)$ satisfying $μ = \frac{k - 1}{2}$ , where $k \geq 5$ is odd. We prove tha…

math.CO2026

Kleitman's theorem over vector spaces: parity phenomena in canonical and global stability

Chenhui Lv, Zixiang Xu

In 1966, Kleitman determined the maximum size of a family of subsets of $[n]$ with bounded symmetric difference. Liao, Liu and Yan recently established a vector-space analogue in t…

math.CO2026

On the characterization of geometric distance-regular graphs

Chenhui Lv, Jack H. Koolen

In 2010, Koolen and Bang proposed the following conjecture: For a fixed integer $m \geq 2$ , any geometric distance-regular graph with smallest eigenvalue $- m$ , diameter $D \geq 3$ …

math.CO2025

Comparing classes of highly symmetric graphs: From $2$ -arc-transitive to $2$ -distance-transitive

Wei Jin, Jack H. Koolen, Chenhui Lv

A $2$ -distance-transitive graph is a vertex-transitive graph whose vertex stabilizer is transitive on both the first- and second-step neighborhoods. This concept simultaneously gen…

math.CO2025

An improved bound for strongly regular graphs with smallest eigenvalue $- m$

Jack Koolen, Chenhui Lv, Greg Markowsky +1

In 1979, Neumaier gave a bound on $λ$ in terms of $m$ and $μ$ , where $- m$ is the smallest eigenvalue of a primitive strongly regular graph, unless the graph in question belongs to…

math.CO2025

A Bose-Laskar-Hoffman theory for $μ$ -bounded graphs with fixed smallest eigenvalue

Jack H. Koolen, Hong-Jun Ge, Chenhui Lv +1

In 2018, by Ramsey and Hoffman theory, Koolen, Yang, and Yang presented a structural result on graphs with smallest eigenvalue at least $- 3$ and large minimum degree. In this study…

math.CO2024

A characterization of the Grassmann graphs: one missing case

Jack H. Koolen, Chenhui Lv, Alexander L. Gavrilyuk

We prove that the Grassmann graphs $J_{2} (2 D + 3, D)$ , $D \geq 3$ , are characterized by their intersection numbers, which settles one of the few remaining cases.

math.CO2024

Bounding the parameter $β$ of a distance-regular graph with classical parameters

Chenhui Lv, Jack H. Koolen

Let $Γ$ be a distance-regular graph with classical parameters $(D, b, α, β)$ satisfying $b \geq 2$ and $D \geq 3$ . Let $r = 1 + b + b^{2} + \dots + b^{D - 1}$ . In 1999, K. Metsch showed that ther…

Automorphism groups of endomorphism monoids of 0-unit 3-valent circulant digraphs

The Aldous property for normal Cayley graphs on symmetric groups

Amply regular graphs with μ close to half the valency and group divisible designs

Kleitman's theorem over vector spaces: parity phenomena in canonical and global stability

On the characterization of geometric distance-regular graphs

Comparing classes of highly symmetric graphs: From 2-arc-transitive to 2-distance-transitive

An improved bound for strongly regular graphs with smallest eigenvalue −m

A Bose-Laskar-Hoffman theory for μ-bounded graphs with fixed smallest eigenvalue

A characterization of the Grassmann graphs: one missing case

Bounding the parameter β of a distance-regular graph with classical parameters

Automorphism groups of endomorphism monoids of $0$ -unit $3$ -valent circulant digraphs

Amply regular graphs with $μ$ close to half the valency and group divisible designs

Comparing classes of highly symmetric graphs: From $2$ -arc-transitive to $2$ -distance-transitive

An improved bound for strongly regular graphs with smallest eigenvalue $- m$

A Bose-Laskar-Hoffman theory for $μ$ -bounded graphs with fixed smallest eigenvalue

Bounding the parameter $β$ of a distance-regular graph with classical parameters