Lele Liu

activity

20232026

collaborators

Showing math.COShow all

9 papers · 1 filter

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…

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

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