The (a, b)KA Indices of Polycyclic Aromatic Hydrocarbons and Benzenoid Systems

International Journal of Mathematics Trends and Technology (IJMTT)  
© 2019 by IJMTT Journal  
Volume65 Issue11  
Year of Publication : 2019  
Authors : V.R.Kulli 

10.14445/22315373/IJMTTV65I11P512 
MLA Style:V.R.Kulli"The (a, b)KA Indices of Polycyclic Aromatic Hydrocarbons and Benzenoid Systems" International Journal of Mathematics Trends and Technology 65.11 (2019):115120.
APA Style: V.R.Kulli(2019).The (a, b)KA Indices of Polycyclic Aromatic Hydrocarbons and Benzenoid Systems” International Journal of Mathematics Trends and Technology,115120.
Abstract
A chemical graph is a graph such that vertices correspond to the atoms and the edges to the bonds. The graph indices are applied to measure the chemical characteristics of compounds in Chemical Graph Theory. In this paper, we introduce the first and second (a, b)KA indices of a chemical graph. Furthermore, we study the mathematical properties of these indices for polycyclic aromatic hydrocarbons and benzenoid systems.
Reference
[1] I. Gutman and O.E. Polansky, Mathematical Concepts in Organic Chemistry, Springer, Berlin (1986).
[2] V.R. Kulli, Multiplicative Connectivity Indices of Nanostructures, LAP LEMBERT Academic Publishing, (2018).
[3] R. Todeschini and V. Consonni, Handbook of Molecular Descriptors for Chemoinformatics, WileyVCH, Weinheim, (2000).
[4] V.R. Kulli, College Graph Theory, Vishwa International Publications, Gulbarga, India (2012).
[5] I. Gutman and N. Trinajstić, Graph theory and molecular orbitals. Total electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17, (1972) 535538.
[6] T. Doslic, B. Furtula, A. Graovać, I Gutman, S. Moradi and Z. Yarahmadi, On vertex degree based molecular structure descriptors, MATCH Commun. Math. Comput. Chem. 66(2011) 613626.
[7] S. Nikolić, G. Kovaćević, A. Milićević and N. Trinajstić, The Zagreb indices 30 years after, Croatica Chemica Acta CCACAA 76(2), (2003) 113124.
[8] K.C. Das and I. Gutman, Some properties of the second Zagreb index, MATCH Commun. Math. Comput. Chem. 52 (2004) 103 112.
[9] B. Borevićanin, K.C. Das, B. Furtula and I. Gutman, Bounds for Zagreb indices, MATCH Commun. Math. Comput. Chem. 78(2017) 17100.
[10] V.R. Kulli, On KV indices and their polynomials of two families of dendrimers, International Journal of Current Research in Life Sciences, 7(9) (2018) 27392744.
[11] V.R. Kulli, Neighborhood Dakshayani indices, International Journal of Mathematical Archive, 10(7) (2019) 2331.
[12] V.R. Kulli, Revan indices and their polynomials of certain rhombus networks, International Journal of Current Research in Life Sciences, 7(5) (2018) 21102116.
[13] G.H. Shirdel, H. Rezapour and A.M. Sayadi, The hyperZagreb index of graph operations, Iranian J. Math. Chem. 4(2) (2013) 213220.
[14] I. Gutman, On hyperZagreb index and coindex, Bull. Acad. Serbe Sci. Arts Cl. Sci. Math. Natur. 150(2017) 18.
[15] F. Falahati Nezhad and M. Azari, Bounds on the hyper Zagreb index, J.Appl.Math. Inform. 34 (2016) 319330.
[16] W. Gao, M.R. Farahari, M. K. Siddiqui and M. K. Jamil, On the first and second Zagreb and first and second hyper Zagreb indices of carbon nanocones CNCk[n], J. Comput. Theor. Nanosci. 13 (2016) 74757482.
[17] V.R. Kulli, Leap hyper Zagreb indices and their polynomials of certain graphs, International Journal of Current Research in Life Sciences, 7(10) (2018) 27832791.
[18] V.R. Kulli, On hyper KV and square KV indices and their polynomials of certain families of dendrimers, Journal of Computer and Mathematical Sciences, 10(2) (2019) 279286.
[19] V.R. Kulli, Some new topological indices of graphs, International Journal of Mathematical Archive, 10(5) (2019) 6270.
[20] V.R. Kulli, Some new status indices of graphs, International Journal of Mathematics Trends and Technology, 65(10) (2019) 7076.
[21] X. Li and H. Zhao, Trees with the first three smallest and largest generalized topological indices, MATCH Commun. Math. Comput. Chem. 50(2004) 5762.
[22] X. Li and J. Zheng, A unified approach to the external trees for different indices, MATCH Commun. Math. Comput. Chem. 54 (2005) 195208.
[23] B. Zhou and N. Trinajstic, On a novel connectivity index, J. Math. Chem. 46(2009) 12521270.
[24] B. Furtula and I. Gutman, A forgotten topological index, J. Math. Chem. 53 (2015), 11841190.
[25] S. Ghobadi and M. Ghorbaninejad, The forgotten topological index for four operations on some special graphs, Bull. Math. Sci. Appl. 16(2016) 8995.
[26] Z. Che and Z. Chen, Lower and upper bounds for the forgotten topological index, MATCH Commun, Math. Comput. Chem. 76 (2016) 63564
[27] B. Zhou and N. Trinajstic, On a novel connectivity index, J. Math. Chem. 46 (2009) 12521270.
[28] M. Randić, On characterization of molecular branching, J. AM. Chem. Sec. 97 (1975) 66096615.
[29] X. Li and I. Gutman, Mathematical Aspects of Randićtype Molecular Structure Descriptors, University Kragujevac, Kragujevac, 2006.
[30] V.R. Kulli, New connectivity topological indices, Annals of Pure and Applied Mathematics, 20(1) (2019) 18.
[31] V.R. Kulli, On connectivity KV indices of certain families of dendrimers, International Journal of Mathematical Archive, 10(2) (2019) 1417.
[32] V.R. Kulli, Connectivity neighborhood Dakshayani indices of POPAM dendrimers, Annals of Pure and Applied Mathematics 20(1) (2019) 4954.
Keywords
Chemical graph, first (a, b)KA index, second (a, b)KA index, polycyclic aromatic hydrocarbon, benzenoid system.