Haiying Shan

works on

diophantine equations 1 equitable partitions 1 main eigenvalues 1 spectral graph theory 1 trees 1

From the 1 of 3 linked papers with an AI index.

collaborators

3 papers

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

The paper classifies all trees of diameter five that have exactly three main eigenvalues, showing they are either symmetric trees T_r(a) or belong to a parametric family defined by…

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…

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

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