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Journal of Combinatorial Optimization

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02-05-2018

New lower bounds for the second variable Zagreb index

Authors: Álvaro Martínez-Pérez, José M. Rodríguez

Published in: Journal of Combinatorial Optimization | Issue 1/2018

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Abstract

The aim of this paper is to obtain new sharp inequalities for a large family of topological indices, including the second variable Zagreb index \(M_2^{\alpha }\), and to characterize the set of extremal graphs with respect to them. Our main results provide lower bounds on this family of topological indices involving just the minimum and the maximum degree of the graph. These inequalities are new even for the Randić, the second Zagreb and the modified Zagreb indices.

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Andova V, Petrusevski M (2011) Variable Zagreb indices and Karamata’s inequality. MATCH Commun Math Comput Chem 65:685–690MathSciNetMATH

Drmota M (2009) Random trees. An interplay between combinatorics and probability. Springer, Wien-New YorkMATH

Fajtlowicz S (1987) On conjectures of Graffiti-II. Congr Numer 60:187–197MathSciNetMATH

Ghorbani M, Songhori M, Gutman I (2012) Modified Narumi–Katayama index. Kragujevac J Sci 34:57–64

Gutman I (2013) Degree-based topological indices. Croat Chem Acta 86:351–361CrossRef

Gutman I, Das KC (2004) The first Zagreb index 30 years after. MATCH Commun Math Comput Chem 50:83–92MathSciNetMATH

Gutman I, Réti T (2014) Zagreb group indices and beyond. Int J Chem Model 6(2–3):191–200

Gutman I, Tošović J (2013) Testing the quality of molecular structure descriptors. Vertex-degreebased topological indices. J Serb Chem Soc 78(6):805–810CrossRef

Gutman I, Trinajstić N (1972) Graph theory and molecular orbitals. Total \(\pi \)-electron energy of alternant hydrocarbons. Chem Phys Lett 17:535–538CrossRef

Kulli VR (2016) Multiplicative connectivity indices of certain nanotubes. Ann Pure Appl Math 12(2):169–176CrossRef

Li X, Zhao H (2004) Trees with the first smallest and largest generalized topological indices. MATCH Commun Math Comput Chem 50:57–62MathSciNetMATH

Li X, Zheng J (2005) A unified approach to the extremal trees for different indices. MATCH Commun Math Comput Chem 54:195–208MathSciNetMATH

Liu M, Liu B (2010) Some properties of the first general Zagreb index. Australas J Combin 47:285–294MathSciNetMATH

Martínez-Pérez A, Rodríguez JM (2018) New lower bounds for the geometric-arithmetic index. MATCH Commun Math Comput Chem 79(2):451–466MathSciNet

Miličević A, Nikolić S (2004) On variable Zagreb indices. Croat Chem Acta 77:97–101

Miličević A, Nikolić S, Trinajstić N (2004) On reformulated Zagreb indices. Mol Divers 8:393–399CrossRef

Milovanović EI, Milovanović IŽ, Dolićanin EĆ, Glogić E (2016) A note on the first reformulated Zagreb index. Appl Math Comput 273:16–20MathSciNet

Nikolić S, Kovačević G, Miličević A, Trinajstić N (2003) The Zagreb indices 30 years after. Croat Chem Acta 76:113–124

Nikolić S, Miličević A, Trinajstić N, Jurić A (2004) On use of the variable Zagreb \(^\nu M_2\) index in QSPR: boiling points of Benzenoid hydrocarbons. Molecules 9:1208–1221CrossRef

Randić M (1975) On characterization of molecular branching. J Am Chem Soc 97:6609–6615CrossRef

Randić M (1991a) Novel graph theoretical approach to heteroatoms in QSAR. Chemometrics Intel Lab Syst 10:213–227

Randić M (1991b) On computation of optimal parameters for multivariate analysis of structure-property relationship. J Chem Inf Comput Sci 31:970–980

Randić M, Plavšić D, Lerš N (2001) Variable connectivity index for cycle-containing structures. J Chem Inf Comput Sci 41:657–662CrossRef

Ranjini PS, Lokesha V, Usha A (2013) Relation between phenylene and hexagonal squeeze using harmonic index. Int J Appl Graph Theory 1:116–121

Rodríguez JM, Sigarreta JM (2017) New results on the harmonic index and its generalizations. MATCH Commun Math Comput Chem 78(2):387–404MathSciNet

Sigarreta JM (2015) Bounds for the geometric–arithmetic index of a graph. Miskolc Math Notes 16:1199–1212MathSciNetCrossRefMATH

Singh M, Ch. Das K, Gupta S, Madan AK (2014) Refined variable Zagreb indices: highly discriminating topological descriptors for QSAR/QSPR. Int J Chem Model 6(2–3):403–428

Vukičević D (2010) Bond additive modeling 2. Mathematical properties of max–min rodeg index. Croat Chem Acta 83(3):261–273

Wiener H (1947) Structural determination of paraffin boiling points. J Am Chem Soc 69:17–20CrossRef

Zhang H, Zhang S (2006) Unicyclic graphs with the first three smallest and largest values of the first general Zagreb index. MATCH Commun Math Comput Chem 55:427–438MathSciNetMATH

Zhang S, Wang W, Cheng TCE (2006) Bicyclic graphs with the first three smallest and largest values of the first general Zagreb index. MATCH Commun Math Comput Chem 55:579–592MathSciNetMATH

Zhou B, Trinajstić N (2010) On general sum-connectivity index. J Math Chem 47:210–218MathSciNetCrossRefMATH

Title: New lower bounds for the second variable Zagreb index
Authors: Álvaro Martínez-Pérez
José M. Rodríguez
Publication date: 02-05-2018
Publisher: Springer US
Published in: Journal of Combinatorial Optimization / Issue 1/2018
Print ISSN: 1382-6905
Electronic ISSN: 1573-2886
DOI: https://doi.org/10.1007/s10878-018-0293-7

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