On the Main Signless Laplacian Eigenvalues of a Graph

2012/08/29 by Hanyuan Deng, He Huang, Deng, Hanyuan +1
Chemistry · Materials Science · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Graphene research and applications #Synthesis and Properties of Aromatic Compounds

paper · pdf · doi:10.48550/arxiv.1208.5835

openalex publication_date 2012/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A signless Laplacian eigenvalue of a graph G is called a main signless Laplacian eigenvalue if it has an eigenvector the sum of whose entries is not equal to zero. In this paper, we first give the necessary and sufficient conditions for a graph with one main signless Laplacian eigenvalue or two main signless Laplacian eigenvalues, and then characterize the trees and unicyclic graphs with exactly two main signless Laplacian eigenvalues, respectively.

Related

• Bicyclic graphs with exactly two main signless Laplacian eigenvalues
• Graphs with zero as a main eigenvalue of the signless Laplacian
• A conjecture on square roots of Laplacian and signless Laplacian eigenvalues of graphs
• A lower bound of the least signless Laplacian eigenvalue of a graph
• Eigenvalue bounds for the signless p-Laplacian