Generalizations of Szőkefalvi Nagy and Chebyshev inequalities with applications in spectral graph theory

Ivan Gutman; Kinkar Ch. Das; Boris Furtula; Emina Milovanović; Igor Milovanović

doi:10.1016/j.amc.2017.05.064

Generalizations of Szőkefalvi Nagy and Chebyshev inequalities with applications in spectral graph theory

Ivan Gutman, Kinkar Ch. Das, Boris Furtula, Emina Milovanović, Igor Milovanović

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

Abstract

Two weighted inequalities for real non-negative sequences are proven. The first one represents a generalization of the Szőkefalvi Nagy inequality for the variance, and the second a generalization of the discrete Chebyshev inequality for two real sequences. Then, the obtained inequalities are used to determine lower bounds for some degree-based topological indices of graphs.

Original language	English
Pages (from-to)	235-244
Number of pages	10
Journal	Applied Mathematics and Computation
Volume	313
DOIs	https://doi.org/10.1016/j.amc.2017.05.064
State	Published - 15 Nov 2017

Keywords

Chebyshev inequality
Degree–based topological index
Szőkefalvi Nagy inequality
Topological index
Zagreb indices

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10.1016/j.amc.2017.05.064

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title = "Generalizations of Sz{\H o}kefalvi Nagy and Chebyshev inequalities with applications in spectral graph theory",

abstract = "Two weighted inequalities for real non-negative sequences are proven. The first one represents a generalization of the Sz{\H o}kefalvi Nagy inequality for the variance, and the second a generalization of the discrete Chebyshev inequality for two real sequences. Then, the obtained inequalities are used to determine lower bounds for some degree-based topological indices of graphs.",

keywords = "Chebyshev inequality, Degree–based topological index, Sz{\H o}kefalvi Nagy inequality, Topological index, Zagreb indices",

author = "Ivan Gutman and \{Ch. Das\}, Kinkar and Boris Furtula and Emina Milovanovi{\'c} and Igor Milovanovi{\'c}",

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AU - Gutman, Ivan

AU - Ch. Das, Kinkar

AU - Furtula, Boris

AU - Milovanović, Emina

AU - Milovanović, Igor

PY - 2017/11/15

Y1 - 2017/11/15

N2 - Two weighted inequalities for real non-negative sequences are proven. The first one represents a generalization of the Szőkefalvi Nagy inequality for the variance, and the second a generalization of the discrete Chebyshev inequality for two real sequences. Then, the obtained inequalities are used to determine lower bounds for some degree-based topological indices of graphs.

AB - Two weighted inequalities for real non-negative sequences are proven. The first one represents a generalization of the Szőkefalvi Nagy inequality for the variance, and the second a generalization of the discrete Chebyshev inequality for two real sequences. Then, the obtained inequalities are used to determine lower bounds for some degree-based topological indices of graphs.

KW - Chebyshev inequality

KW - Degree–based topological index

KW - Szőkefalvi Nagy inequality

KW - Topological index

KW - Zagreb indices

UR - https://www.scopus.com/pages/publications/85020853637

U2 - 10.1016/j.amc.2017.05.064

DO - 10.1016/j.amc.2017.05.064

M3 - Article

AN - SCOPUS:85020853637

SN - 0096-3003

VL - 313

SP - 235

EP - 244

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

ER -

Generalizations of Szőkefalvi Nagy and Chebyshev inequalities with applications in spectral graph theory

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Keywords

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