International Journal of Mathematics Trends and Technology
Volume 56 | Number 7 | Year 2018 | Article Id. IJMTT-V56P567 | DOI : https://doi.org/10.14445/22315373/IJMTT-V56P567
The first Zagreb index 1 M (G ) is equal to the sum of squares of the degrees of the vertices, and the second Zagreb index 2 M (G ) is equal to the sum of the products of the degrees of pairs of adjacent vertices of the underlying molecular graph G. In this paper we give some new bounds for the first and second general Zagreb indices 1 M ( G) and 2 M (G ) .
[1] I. Gutman and N. Trinajstić, Graph theory and molecular orbitals, Total -electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972) 535--538.
[2] I. Gutman, B. Ruščić, N. Trinajstić and C. F. Wilcox, Graph theory and molecular orbitals, XII. Acyclic polyenes, J. Chem. Phys. 62 (1975) 3399--3405.
[3] T. Balaban, I.Motoc, D. Bonchev and O.Mekenyan, Topological indices for structure activity correlations, Topics Curr. Chem. 114 (1983), 21 - 55.
[4] T. Balaban, I. Motoc, D. Bonchev and O. Mekenyan, Topological indices for structure activity correlations, Topics Curr. Chem. 114 (1983) 21--55.
[5] R. Todeschini and V. Consoni, Handbook of Molecular Descriptors, Wiley-VCH, New York, 2002.
[6] S. Nikolić G. Kovačević and A. Miličević, The Zagreb indices 30 years after, Croat. Chem. Acta. 76 (2003) 113--124.
[7] I. Gutman, K.C. Das, The first Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem. 50 (2004) 83--92.
[8] A. Miličević, S. Nikolić, On Variable Zagreb indices, Croat. Chem. Acta 77 (2003) 97--101.
[9] X. Li and J. Zheng, A unified approach to the extremal trees for different indices, MATCH Commun. Math. Comput. Chem. 54 (2005) 195--208.
[10] G. Britto Antony Xavier, E. Suresh and I. Gutman, Counting relations for general Zagreb indices, Kragujevac Journal of Math. 38 (2014) 95--103.
[11] X. Li and H. Zhao, Trees with the first smallest and largest generalized topological indices, MATCH Commun. Math. Comput. Chem. 50 (2004) 57--62.
[12] H. Zhang and S. Zhang, Unicyclic graphs with the first three smallest and largest values of the first general Zagreb index, MATCH Commun. Math. Comput. Chem. 55 (2006) 427--438.
[13] S. Zhang, W. Wang and T.C.E. Cheng, Bicyclic graphs with the first three smallest and largest values of the first general Zagreb index, MATCH Commun. Math. Comput. Chem. 55 (2006) 579--592.
[14] M. Liu and B. Liu, Some properties of the first general Zagreb index, Australas. J. Combin. 47 (2010) 285--294.
[15] A. Ilić and D.Stevanović On comparing Zagreb indices, MATCH Commun. Math. Comput. Chem. 62 (2009), 681 - 687.
[16] D. de Caen, An upper bound on the sum of squares of degrees in a graph, Discr. Math. 185 (1998), 245 - 248.
A. Selvakumar, K. Agilarasan, "Bounds on General Zagreb Indices," International Journal of Mathematics Trends and Technology (IJMTT), vol. 56, no. 7, pp. 524-526, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V56P567
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