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Operations Research Transactions >

2025 , Vol. 29 >Issue 1: 185 - 197

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2025.01.015

The extremal k-uniform hypergraphs with given number of pendent vertices on signless Laplacian spectral radius

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  • 1. Psychological Fitness Teaching and Research Center, Yunnan Police College, Kunming 650221, Yunnan, China
    2. School of Mathematics and Statistics, South-Central University for Nationalities, Wuhan 430074, Hubei, China

Received date: 2021-12-01

  Online published: 2025-03-08

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, 2025, All rights reserved. Unauthorized reproduction is prohibited.
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Abstract

For a $k$-uniform hypergraph $H=(V, E)$, let $B(H)$ be its incidence matrix and $\mathcal{Q}(H)=B(H)B(H)^{\top}$ be its signless Laplacian matrix. The signless Laplacian spectral radius of $H$ is the maximum modulus of all eigenvalues of $\mathcal{Q}(H)$. Let $\mathcal{H}^n_{k, r}$ be the class of connected $k$-uniform hypergraphs with $n$ vertices and $r$ pendent vertices. In this paper, the extremal hypergraphs having maximum spectral radii in $\mathcal{H}^n_{k, r}$ are characterized for $n-r\geq k$ and some cases $n-r\in [k-1]$, respectively.

Key words： k-uniform hypergraph; signless Laplacian spectral radius; principal eigenvector

Cite this article

Yu YANG, Zhongxun ZHU, Junpeng ZHOU . The extremal k-uniform hypergraphs with given number of pendent vertices on signless Laplacian spectral radius[J]. Operations Research Transactions, 2025 , 29(1) : 185 -197 . DOI: 10.15960/j.cnki.issn.1007-6093.2025.01.015

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