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Symmetry
Volume 12
Issue 7
10.3390/sym12071097
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Article

New Bounds for Topological Indices on Trees through Generalized Methods

by
Álvaro Martínez-Pérez
1 and
José M. Rodríguez
2,*
1
Departamento de Análisis Económico y Finanzas, Universidad de Castilla-La Mancha, Avda. Real Fábrica de Sedas s/n, 45600 Talavera de la Reina, Spain
2
Departamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, Leganés, 28911 Madrid, Spain
*
Author to whom correspondence should be addressed.
Symmetry 2020, 12(7), 1097; https://doi.org/10.3390/sym12071097
Submission received: 3 June 2020 / Revised: 22 June 2020 / Accepted: 26 June 2020 / Published: 2 July 2020
(This article belongs to the Special Issue Analytical and Computational Properties of Topological Indices)
Versions Notes

Abstract

Topological indices are useful for predicting the physicochemical behavior of chemical compounds. A main problem in this topic is finding good bounds for the indices, usually when some parameters of the graph are known. The aim of this paper is to use a unified approach in order to obtain several new inequalities for a wide family of topological indices restricted to trees and to characterize the corresponding extremal trees. The main results give upper and lower bounds for a large class of topological indices on trees, fixing or not the maximum degree. This class includes the first variable Zagreb, the Narumi–Katayama, the modified Narumi–Katayama and the Wiener index.
Keywords: first variable zagreb index; Narumi–Katayama index; modified Narumi–Katayama index; Wiener index; topological indices; Schur-convexity; trees first variable zagreb index; Narumi–Katayama index; modified Narumi–Katayama index; Wiener index; topological indices; Schur-convexity; trees

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MDPI and ACS Style

Martínez-Pérez, Á.; Rodríguez, J.M. New Bounds for Topological Indices on Trees through Generalized Methods. Symmetry 2020, 12, 1097. https://doi.org/10.3390/sym12071097

AMA Style

Martínez-Pérez Á, Rodríguez JM. New Bounds for Topological Indices on Trees through Generalized Methods. Symmetry. 2020; 12(7):1097. https://doi.org/10.3390/sym12071097

Chicago/Turabian Style

Martínez-Pérez, Álvaro, and José M. Rodríguez. 2020. "New Bounds for Topological Indices on Trees through Generalized Methods" Symmetry 12, no. 7: 1097. https://doi.org/10.3390/sym12071097

APA Style

Martínez-Pérez, Á., & Rodríguez, J. M. (2020). New Bounds for Topological Indices on Trees through Generalized Methods. Symmetry, 12(7), 1097. https://doi.org/10.3390/sym12071097

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