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The spectral Erdős book theorem: sharp bounds and stability
Lele Liu, Yongtao Li, Bo Ning
The booksize of a graph is the largest number of triangles sharing a common edge. A classical theorem of Edwards, conjectured by Bollobás and Erdős, states tha…
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 vertices is the unique planar graph of maximum adjacency spectral radius…
The largest Laplacian eigenvalue of induced--free graphs
Lele Liu, Bo Ning
Let be a simple graph of maximum degree , and let denote the largest eigenvalue of its Laplacian matrix. For a fixed integer , Aharoni, Alon, and Berger (201…
Maximum spectral sum of graphs
Hitesh Kumar, Lele Liu, Hermie Monterde +2
For a graph of order , the spectral sum of is defined to be the sum , where (resp. ) is the largest (resp. second largest) adjacency ei…
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 is a connected graph with the unit Perron vector , then any independent set of satisfies $\sum_{v\in S} x_v^2 \l…
A short proof of a perturbation inequality for the spectral radius
Lele Liu, Bo Ning
Let be a simple graph, and denote by its spectral radius. Sun and Das (2020) established that for any non-isolated vertex with degree , \[ λ(G)\leq \sqrt{λ(G-v…