Author

Haiying Shan

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Preprint Sep 2026

Uniform Hypergraphs with $\alpha$-Spectral Radius at Most That of a Loose Cycle

Let $k\geq 3$ and $\alpha\in[0,1)$, and let $\lambda_k(\alpha)$ denote the $\alpha$-spectral radius of a $k$-uniform loose cycle. Lu and Man classified all connected $k$-uniform hypergraphs with adjacency spectral radius at most $\lambda_k(0)$. In this paper, we extend their classification to the $\alpha$-spectral sett...

Hang-Xi Cha, Xiao-Qi Liu, H. Shan · 0 citations

Preprint Jul 2026

Graphs with zero as a main eigenvalue of the signless Laplacian

An eigenvalue of the signless Laplacian $Q(G)$ is $Q$-main if its eigenspace is not orthogonal to the all-ones vector. We characterize graphs with exactly $\ell\ge3$ $Q$-main eigenvalues, one of which is zero. The case $\ell=3$ reduces to non-semiregular bipartite graphs satisfying a vertexwise signed degree-sum identi...

Hangxi Cha, Haiying Shan · 0 citations

Preprint Jul 2026

Trees with exactly three main eigenvalues

An eigenvalue of a graph is called main if its eigenspace is not orthogonal to the all-ones vector. Introduced by Cvetkovi\'{c} in the early 1970s and systematically studied by Rowlinson and others, graphs with exactly one or two main eigenvalues are now well understood. However, the classification of graphs with preci...

Hang-Xi Cha, H. Shan · 0 citations