Lower bounds for Laplacian spread and relations with invariant parameters revisited

2018/05/30 by Enide Andrade, Andrade, Enide, Maria Aguieiras A. de Freitas +5
Materials Science · Mathematics · #Combinatorics (math.CO) #Dendrimers and Hyperbranched Polymers #FOS: Mathematics #Graph theory and applications #Graphene research and applications #Spectral Theory (math.SP) #math.CO #math.SP

paper · pdf · doi:10.48550/arxiv.1805.12250

arxiv created 2018/05/30 · openalex publication_date 2018/05/30 · arxiv updated 2018/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G=( V( G) ,E( G) ) be an ( n,m) -graph and X a nonempty proper subset of V( G) . Let X^c=V( G) \backslash X. The edge density of X in G is given by ρ_G( X) =\fracn\vert E_X( G) \vert \vert X\vert \vert X^c\vert , where E_X( G) is the set of edges in G with one end in % X and the other in X^c. The Laplacian spread of a graph is the difference between the greatest Laplacian eigenvalue and the algebraic connectivity. In this paper, we use the edge density of some nonempty proper subsets of vertices in G to establish new lower bounds for the Laplacian spread. Also, using some known numerical inequalities some lower bounds for the Laplacian spread of a graph with a prescribed degree sequence are presented.

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