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

Autor: Hongye Song, Huicai Jia
Rok vydání: 2018
Předmět:
Mathematics::Analysis of PDEs
010103 numerical & computational mathematics
0102 computer and information sciences
Distance eigenvalues
01 natural sciences
Combinatorics
Computer Science::General Literature
Discrete Mathematics and Combinatorics
0101 mathematics
ComputingMilieux_MISCELLANEOUS
Eigenvalues and eigenvectors
Connectivity
Mathematics
lcsh:Mathematics
Research
Computer Science::Information Retrieval
Applied Mathematics
Astrophysics::Instrumentation and Methods for Astrophysics
Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing)
Mathematics::Spectral Theory
lcsh:QA1-939
Remoteness
Signless laplacian
Graph
Vertex (geometry)
TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES
010201 computation theory & mathematics
ComputingMethodologies_DOCUMENTANDTEXTPROCESSING
05C50
Distance (signless) Laplacian eigenvalues
Laplace operator
Analysis
Zdroj: Journal of Inequalities and Applications
Journal of Inequalities and Applications, Vol 2018, Iss 1, Pp 1-12 (2018)
ISSN: 1029-242X
DOI: 10.1186/s13660-018-1663-5
Popis: 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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\partial_{1}\geq\cdots\geq\partial_{n}$\end{document}∂1≥⋯≥∂n, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\partial_{1}^{L}\geq\cdots\geq\partial_{n}^{L}$\end{document}∂1L≥⋯≥∂nL and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\partial_{1} ^{Q}\geq\cdots\geq\partial_{n}^{Q}$\end{document}∂1Q≥⋯≥∂nQ be the distance, distance Laplacian and distance signless Laplacian eigenvalues of G, respectively. In this paper, we give lower bounds on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\rho+\partial _{1}$\end{document}ρ+∂1, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\rho-\partial_{n}$\end{document}ρ−∂n, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\rho+\partial_{1}^{L}$\end{document}ρ+∂1L, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\partial_{1} ^{L}-\rho$\end{document}∂1L−ρ, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$2\rho+\partial_{1}^{Q}$\end{document}2ρ+∂1Q and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\partial_{1}^{Q}-2\rho$\end{document}∂1Q−2ρ and the corresponding extremal graphs are also characterized.
Databáze: OpenAIRE
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