Author

Ze-Jun Huang

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Preprint Sep 2026

Extremal spectral radius of nonregular graphs with a fixed odd maximum degree

For integers $n\ge3$ and $2\le\Delta\le n-1$, let $\lambda_1(n,\Delta)$ be the maximum adjacency spectral radius among all connected nonregular graphs of order $n$ and maximum degree $\Delta$. Liu conjectured that for each fixed integer $\Delta\ge3$, \[ \lim_{n\to\infty}n^2\bigl(\Delta-\lambda_1(n,\Delta)\bigr)= \begin...

Ze-Jun Huang, Chen-Xi Yang · 0 citations

Preprint Oct 2026

Degree sequences of spectrally extremal connected nonregular graphs with prescribed maximum degree: the dense case

Let $G$ be an $n$-vertex connected nonregular graph with maximum degree $\Delta$ that attains the maximum spectral radius. For $3\le\Delta\le n-2$, Liu and Li (2008) conjectured that $G$ has the degree sequence $(\Delta,\ldots,\Delta,\delta)$ with $\delta<\Delta$ as large as possible. In this paper, we study the dense...

Ze-Jun Huang, Chen-Xi Yang · 0 citations