Lele Liu

activity

20232026

most citedVariants of spectral Turán theorems and eigenvectors of graphs

1 citations · 1 across the 9 of their papers we have counts for

collaborators

10 papers

math.CO2026

The spectral Erdős book theorem: sharp bounds and stability

Lele Liu, Yongtao Li, Bo Ning

The booksize $bk (G)$ of a graph $G$ is the largest number of triangles sharing a common edge. A classical theorem of Edwards, conjectured by Bollobás and Erdős, states tha…

math.CO2026

A complete solution to the Boots-Royle/Cao-Vince conjecture

Lele Liu, Bo Ning, Yi Wang

Boots and Royle, and independently Cao and Vince, conjectured that the join of an edge and a path on $n - 2$ vertices is the unique planar graph of maximum adjacency spectral radius…

math.CO2026

The largest Laplacian eigenvalue of induced- $K_{1, r}$ -free graphs

Lele Liu, Bo Ning

Let $G$ be a simple graph of maximum degree $d$ , and let $μ (G)$ denote the largest eigenvalue of its Laplacian matrix. For a fixed integer $k \geq 2$ , Aharoni, Alon, and Berger (201…

math.CO2026

Maximum spectral sum of graphs

Hitesh Kumar, Lele Liu, Hermie Monterde +2

For a graph $G$ of order $n$ , the spectral sum of $G$ is defined to be the sum $λ_{1} (G) + λ_{2} (G)$ , where $λ_{1} (G)$ (resp. $λ_{2} (G)$ ) is the largest (resp. second largest) adjacency ei…

math.CO2026

An exponentially small gap of the Perron vector on independent sets

Hongzhang Chen, Jianxi Li, Yongtao Li +2

A classical result of Cioabă states that if $G$ is a connected graph with the unit Perron vector $x$ , then any independent set $S$ of $G$ satisfies $\sum_{v\in S} x_v^2 \l…

math.CO2026

A short proof of a perturbation inequality for the spectral radius

Lele Liu, Bo Ning

Let $G$ be a simple graph, and denote by $λ (G)$ its spectral radius. Sun and Das (2020) established that for any non-isolated vertex $v$ with degree $d (v)$ , \[ λ(G)\leq \sqrt{λ(G-v…

math.CO2025

A new spectral Turán theorem for weighted graphs and consequences

Lele Liu, Bo Ning

Confirming a conjecture of Elphick and Edwards and strengthening a spectral theorem of Wilf, Nikiforov proved that for any $K_{r + 1}$ -free graph $G$ , $λ (G)^{2} \leq 2 (1 - 1/ r) m$ , wh…

math.CO2024

Hypergraph Extensions of Spectral Turán Theorem

Lele Liu, Zhenyu Ni, Jing Wang +1

The spectral Turán theorem states that the $k$ -partite Turán graph is the unique graph attaining the maximum adjacency spectral radius among all graphs of order $n$ containing no t…

math.CO2024

A characterization of extremal non-transmission-regular graphs by the distance (signless Laplacian) spectral radius

Jingfen Lan, Lele Liu

Let $G$ be a simple connected graph of order $n$ and $\partial (G)$ is the spectral radius of the distance matrix $D (G)$ of $G$ . The transmission $D_{i}$ of vertex $i$ is the $i$ -th r…

math.CO2023★ 1 cited

Variants of spectral Turán theorems and eigenvectors of graphs

Lele Liu, Bo Ning

In 2002, Nikiforov proved that for an $n$ -vertex graph $G$ with clique number $ω$ and edge number $m$ , the spectral radius $λ (G)$ satisfies $λ (G) \leq 2 (1 - 1/ ω) m$ , which c…

The spectral Erdős book theorem: sharp bounds and stability

A complete solution to the Boots-Royle/Cao-Vince conjecture

The largest Laplacian eigenvalue of induced-K1,r​-free graphs

Maximum spectral sum of graphs

An exponentially small gap of the Perron vector on independent sets

A short proof of a perturbation inequality for the spectral radius

A new spectral Turán theorem for weighted graphs and consequences

Hypergraph Extensions of Spectral Turán Theorem

A characterization of extremal non-transmission-regular graphs by the distance (signless Laplacian) spectral radius

Variants of spectral Turán theorems and eigenvectors of graphs

The largest Laplacian eigenvalue of induced- $K_{1, r}$ -free graphs