New Bounds for Topological Indices on Trees through Generalized Methods
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 ne...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-07-01
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| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/12/7/1097 |
| _version_ | 1797563484331835392 |
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| author | Álvaro Martínez-Pérez José M. Rodríguez |
| author_facet | Álvaro Martínez-Pérez José M. Rodríguez |
| author_sort | Álvaro Martínez-Pérez |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T18:44:17Z |
| format | Article |
| id | doaj.art-27023cda423f4c76ab8bbcc40533407c |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T18:44:17Z |
| publishDate | 2020-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-27023cda423f4c76ab8bbcc40533407c2023-11-20T05:37:28ZengMDPI AGSymmetry2073-89942020-07-01127109710.3390/sym12071097New Bounds for Topological Indices on Trees through Generalized MethodsÁlvaro Martínez-Pérez0José M. Rodríguez1Departamento de Análisis Económico y Finanzas, Universidad de Castilla-La Mancha, Avda. Real Fábrica de Sedas s/n, 45600 Talavera de la Reina, SpainDepartamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, Leganés, 28911 Madrid, SpainTopological 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.https://www.mdpi.com/2073-8994/12/7/1097first variable zagreb indexNarumi–Katayama indexmodified Narumi–Katayama indexWiener indextopological indicesSchur-convexity |
| spellingShingle | Álvaro Martínez-Pérez José M. Rodríguez New Bounds for Topological Indices on Trees through Generalized Methods Symmetry first variable zagreb index Narumi–Katayama index modified Narumi–Katayama index Wiener index topological indices Schur-convexity |
| title | New Bounds for Topological Indices on Trees through Generalized Methods |
| title_full | New Bounds for Topological Indices on Trees through Generalized Methods |
| title_fullStr | New Bounds for Topological Indices on Trees through Generalized Methods |
| title_full_unstemmed | New Bounds for Topological Indices on Trees through Generalized Methods |
| title_short | New Bounds for Topological Indices on Trees through Generalized Methods |
| title_sort | new bounds for topological indices on trees through generalized methods |
| topic | first variable zagreb index Narumi–Katayama index modified Narumi–Katayama index Wiener index topological indices Schur-convexity |
| url | https://www.mdpi.com/2073-8994/12/7/1097 |
| work_keys_str_mv | AT alvaromartinezperez newboundsfortopologicalindicesontreesthroughgeneralizedmethods AT josemrodriguez newboundsfortopologicalindicesontreesthroughgeneralizedmethods |