Haiying Shan

activity

20232026

collaborators

9 papers

math.CO2026

Spectral Erdős--Gallai Theorems for the $\mathcal A_α$-Tensor of the $s$-Clique Hypergraph

Xiaoqi Liu, Haiying Shan

The Erdős--Gallai theorem determines the maximum number of edges in a graph with bounded matching number; its clique-counting extension replaces edges by $s$ -cliques, and a spectra…

math.CO2026

Asymptotic maximum spectral radius of nonregular graphs

Hangxi Cha, Haiying Shan

Let $λ_{1} (n, Δ)$ be the maximum adjacency spectral radius among connected nonregular simple graphs of order $n$ and maximum degree $Δ$ . Using effective resistance bounds, explicit co…

math.CO2026

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

Hangxi Cha, Xiaoqi Liu, Haiying Shan

Let $k \geq 3$ and $α \in [0, 1)$ , and let $λ_{k} (α)$ denote the $α$ -spectral radius of a $k$ -uniform loose cycle. Lu and Man classified all connected $k$ -uniform hypergraphs with adjace…

math.CO2026

Graphs with zero as a main eigenvalue of the signless Laplacian

Hangxi Cha, Haiying Shan

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 $ℓ \geq 3$ $Q$ -main eigen…

math.CO2026

Trees with exactly three main eigenvalues

Hangxi Cha, Haiying Shan

An eigenvalue of a graph is called main if its eigenspace is not orthogonal to the all-ones vector. Introduced by Cvetković in the early 1970s and systematically studied by Rowlins…

math.CO2024

Exploring Graphs with Distinct $M$ -Eigenvalues: Product Operation, Wronskian Vertices, and Controllability

Haiying Shan, Xiaoqi Liu

Let $G^{M}$ denote the set of connected graphs with distinct $M$ -eigenvalues. This paper explores the $M$ -spectrum and eigenvectors of a new product $G \circ_{C} H$ of graphs…

math.CO2024

Extremal spectral radius of degree-based weighted adjacency matrices of graphs with given order and size

Chenghao Shen, Haiying Shan

The $f$ adjacency matrix is a type of edge-weighted adjacency matrix, whose weight of an edge $ij$ is $f (d_{i}, d_{j})$ , where $f$ is a real symmetric function and $d_{i}, d_{j}$ are the deg…

math.CO2024

The distance spectral radius of $k$ -uniform hypertrees with given number of vertices of maximum degree

Xiaoqi Liu, Haiying Shan

This paper investigates the influence of two graft transformations on the distance spectral radius of connected uniform hypergraphs. Specifically, we study $k$ -uniform hypertrees w…

math.CO2023

On the relationship between shortlex order and $A_{α}$ -spectral radii of graphs with starlike branch tree

Haiying Shan, Muhuo Liu

Let $P (n)$ denote the set of all partitions of $n$ , whose elements are nondecreasing sequences of positive integers whose sum is $n$ . For ${\bf a}=( n_{1}, n_{2},\ldots, n_{d}) \in…

Spectral Erdős--Gallai Theorems for the \(\mathcal A_α\)-Tensor of the \(s\)-Clique Hypergraph

Asymptotic maximum spectral radius of nonregular graphs

Uniform Hypergraphs with α-Spectral Radius at Most That of a Loose Cycle

Graphs with zero as a main eigenvalue of the signless Laplacian

Trees with exactly three main eigenvalues

Exploring Graphs with Distinct M-Eigenvalues: Product Operation, Wronskian Vertices, and Controllability

Extremal spectral radius of degree-based weighted adjacency matrices of graphs with given order and size

The distance spectral radius of k-uniform hypertrees with given number of vertices of maximum degree

On the relationship between shortlex order and Aα​-spectral radii of graphs with starlike branch tree

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

Exploring Graphs with Distinct $M$ -Eigenvalues: Product Operation, Wronskian Vertices, and Controllability

The distance spectral radius of $k$ -uniform hypertrees with given number of vertices of maximum degree

On the relationship between shortlex order and $A_{α}$ -spectral radii of graphs with starlike branch tree