Da Zhao

collaborators

6 papers

math.CO2026

Bipartite graphs, random graphs, and Lin--Lu--Yau curvature

Huiqiu Lin, Zhe You, Da Zhao

Let $G = (X, Y; E)$ be a bipartite graph with parts $X$ and $Y$ where $∣ X ∣ = m$ and $∣ Y ∣ = n$ . We show that every bipartite graph with more than $mn - D (m, n)$ edges has positive Lin--L…

math.CO2026

Almost all graphs have no cospectral mates with height relative small to its order

Da Zhao

The main result of this paper shows that almost all graphs of order $n$ have no cospectral mates with height $o ((n / ln n)^{1/10})$ , improving an earlier result on cospectral mat…

math.CO2025

Estimates of the first Dirichlet eigenvalue of graphs

Huiqiu Lin, Lianping Liu, Zhe You +1

Inspired by the Li--Yau eigenvalue-diameter estimates, we investigate lower bounds for the first Dirichlet eigenvalue in terms of the diameter (or inscribed radius) of a graph. Let…

math.CO2025

Comparison between the first Steklov eigenvalue and algebraic connectivity on trees

Huiqiu Lin, Da Zhao

Trees can be regarded as discrete analogue of Hadamard manifolds, namely simply-connected Riemannian manifolds of non-positive sectional curvature. In this paper, we compare the fi…

math.CO2025

Maximize the Steklov eigenvalue of trees

Huiqiu Lin, Da Zhao

We study the maximal Steklov eigenvalues of trees with given number of boundary vertices and total number of vertices. Trees can be regarded as discrete analogue of Hadamard manifo…

math.CO2025

The first Steklov eigenvalue of planar graphs and beyond

Huiqiu Lin, Da Zhao

The Steklov eigenvalue problem was introduced over a century ago, and its discrete form attracted interest recently. Let $D$ and $I^´ I^c ◯$ be the maximum vertex degree and the set of…