K1 and K2 Indices

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2022 by IJMTT Journal
Volume-68 Issue-1
Year of Publication : 2022
Authors : V.R.Kulli
  10.14445/22315373/IJMTT-V68I1P505

MLA

MLA Style: V.R.Kulli. "K1 and K2 Indices" International Journal of Mathematics Trends and Technology 68.1 (2022):43-52. 

APA Style: V.R.Kulli(2022). K1 and K2 Indices  International Journal of Mathematics Trends and Technology, 68(1), 43-52.

Abstract
In this paper, we introduce the K1 and K2 graphical indices of a graph. We compute these two indices for some standard graphs and certain important chemical structures such as nanostar dendrimers. Also we establish some bounds on these two indices.

Reference

[1] V.R. Kulli, College Graph Theory, Vishwa International Publications, Gulbarga, India (2012).
[2] V.R.Kulli, Graph indices, in Hand Book of Research on Advanced Applications of Application Graph Theory in Modern Society, M. Pal. S. Samanta and A. Pal, (eds.) IGI Global, USA (2020) 66-91.
[3] I. Gutman and O.E. Polansky, Mathematical Concepts in Organic Chemistry, Springer, Berlin (1986).
[4] V.R.Kulli, Multiplicative Connectivity Indices of Nanostructures, LAP LEMBERT Academic Publishing, (2018).
[5] R.Todeschini and V. Consonni, Handbook of Molecular Descriptors for Chemoinformatics, Weinheim, Wiley-VCH, (2009).
[6] M.Randic, On characterization of molecular branching, Journal of American Chemical Society, 97 (1975) 6609-6615.
[7] X.Li and I.Gutman, Mathematical Aspects of Randic Type Molecular Structure Descriptors, Univ. Kragujevac, Kragujevac, (2006).
[8] I.Gutman and B.Furtula, Recent Results in the Theory of Randic Index, Univ. Kragujevac, Kragujevac, (2008).
[9] O.Favaron, M.Maho and F.J.Sacle, Some eigenvalue properties in graphs (conjectures of Graffiti II), discrete Math. 111(1-3) (1993) 197-220.
[10] L.Zhong, The harmonic index for graphs, Appl. Math Lett 25(3) (2012) 561-566.
[11] I.Gutman, V.R.Kulli and I.Redzepocic, Nirmala index of Kragujevac trees, International Journal of Mathematics Trends and Technology, 67(6) (2021) 44-49.
[12] V.R.Kulli, Computation of distance based connectivity status neighborhood Dakshayani indices, International Journal of Mathematics Trends and Technology, 66(6) (2020) 118-128.
[13] V.R.Kulli, Computation of status neighborhood indices of graphs, International Journal of Recent Scientific Research, 11(4) (2020) 38079-38085.
[14] V.R.Kulli, Hyper Zagreb-K-Banhatti indices of graphs, International Journal of Mathematics Trends and Technology, 66(8) (2020) 123-130.
[15] V.R.Kulli, Some new status neighborhood indices of graphs, International Journal of Mathematics Trends and Technology, 66(9) (2020) 139-153.
[16] V.R.Kulli, Harmonic Zagreb-K-Banhatti index of a graph, International Journal of Mathematics Trends and Technology, 66(10) (2020) 123-132.
[17] V.R.Kulli, Neighborhood Sombor index of some nanostructures, International Journal of Mathematics Trends and Technology, 67(5) (2021) 101-108.
[18] V.R.Kulli, Different versions of Nirmala index of certain chemical structures, International Journal of Mathematics Trends and Technology, 67(7) (2021) 56-63.
[19] V.R.Kulli, B.Chaluvaraju and T.Vidya, Computation ofAdriatic (a, b)-KA index of some nanostructures, International Journal of Mathematics Trends and Technology, 67(4) (2021) 79-87.
[20] V.R.Kulli and I.Gutman, (a, b)-KA indices of benzenoid systems, International Journal of Mathematics Trends and Technology, 67(1) (2021) 17-20.
[21] V.R.Kulli, Some new Kulli-Basava topological indices, Earthline Journal of Mathematical Sciences, 2(2) (2019) 343-354.
[22] V.R.Kulli, Contraharmonic-quadratic index of certain nanostar dendrimers, International Journal of Mathematical Archive, 13(1) (2022).
[23] V.R.Kulli, Geometric-quadratic and quadratic-geometric indices, submitted.
[24] V.R.Kulli, ABC Banhatti and augmented Banhatti indices of chemical networks, Journal of Chemistry and Chemical Sciences, 8(8) (2018) 1018-1025.
[25] V.R.Kulli, B.Chaluvaraju, V.Lokesha and S.A.Basha, Gourava indices of some dendrimers, Research Review International Journal of Multidisciplinary, 4(6) (2019) 212-215.

Keywords : molecular structure, K1 index, K2 index, nanostar demdrimer.