Partial characterization of graphs having a single large Laplacian\n eigenvalue

2017/10/04 by Luiz Emílio Allem, Allem, L. Emilio, Antonio Cafure +9
Chemistry · Mathematics · #05C50 #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Metal-Organic Frameworks: Synthesis and Applications #Synthesis and Properties of Aromatic Compounds

paper · pdf · doi:10.48550/arxiv.1710.01710

openalex publication_date 2017/10/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The parameter \σ(G) of a graph G stands for the number of Laplacian\neigenvalues greater than or equal to the average degree of G. In this work,\nwe address the problem of characterizing those graphs G having \σ(G)=1.\nOur conjecture is that these graphs are stars plus a (possible empty) set of\nisolated vertices. We establish a link between \σ(G) and the number of\nanticomponents of G. As a by-product, we present some results which support\nthe conjecture, by restricting our analysis to some classes of graphs.\n

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