Remoteness and distance, distance (signless) Laplacian eigenvalues of a graph

Let G be a connected graph of order n. The remoteness of G, denoted by ρ, is the maximum average distance from a vertex to all other vertices. Let [Formula: see text] , [Formula: see text] and [Formula: see text] be the distance, distance Laplacian and distance signless Laplacian eigenvalues of G, r...

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Detalles Bibliográficos
Autores principales: Jia, Huicai, Song, Hongye
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2018
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5882757/
https://www.ncbi.nlm.nih.gov/pubmed/29628745
http://dx.doi.org/10.1186/s13660-018-1663-5
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author Jia, Huicai
Song, Hongye
author_facet Jia, Huicai
Song, Hongye
author_sort Jia, Huicai
collection PubMed
description Let G be a connected graph of order n. The remoteness of G, denoted by ρ, is the maximum average distance from a vertex to all other vertices. Let [Formula: see text] , [Formula: see text] and [Formula: see text] be the distance, distance Laplacian and distance signless Laplacian eigenvalues of G, respectively. In this paper, we give lower bounds on [Formula: see text] , [Formula: see text] , [Formula: see text] , [Formula: see text] , [Formula: see text] and [Formula: see text] and the corresponding extremal graphs are also characterized.
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spelling pubmed-58827572018-04-05 Remoteness and distance, distance (signless) Laplacian eigenvalues of a graph Jia, Huicai Song, Hongye J Inequal Appl Research Let G be a connected graph of order n. The remoteness of G, denoted by ρ, is the maximum average distance from a vertex to all other vertices. Let [Formula: see text] , [Formula: see text] and [Formula: see text] be the distance, distance Laplacian and distance signless Laplacian eigenvalues of G, respectively. In this paper, we give lower bounds on [Formula: see text] , [Formula: see text] , [Formula: see text] , [Formula: see text] , [Formula: see text] and [Formula: see text] and the corresponding extremal graphs are also characterized. Springer International Publishing 2018-04-03 2018 /pmc/articles/PMC5882757/ /pubmed/29628745 http://dx.doi.org/10.1186/s13660-018-1663-5 Text en © The Author(s) 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Jia, Huicai
Song, Hongye
Remoteness and distance, distance (signless) Laplacian eigenvalues of a graph
title Remoteness and distance, distance (signless) Laplacian eigenvalues of a graph
title_full Remoteness and distance, distance (signless) Laplacian eigenvalues of a graph
title_fullStr Remoteness and distance, distance (signless) Laplacian eigenvalues of a graph
title_full_unstemmed Remoteness and distance, distance (signless) Laplacian eigenvalues of a graph
title_short Remoteness and distance, distance (signless) Laplacian eigenvalues of a graph
title_sort remoteness and distance, distance (signless) laplacian eigenvalues of a graph
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5882757/
https://www.ncbi.nlm.nih.gov/pubmed/29628745
http://dx.doi.org/10.1186/s13660-018-1663-5
work_keys_str_mv AT jiahuicai remotenessanddistancedistancesignlesslaplacianeigenvaluesofagraph
AT songhongye remotenessanddistancedistancesignlesslaplacianeigenvaluesofagraph

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