A note on general sum-connectivity index
DOI:
https://doi.org/10.22199/issn.0717-6279-5676Keywords:
simple graphs, general sum-connectivity index, general Randić indexAbstract
For a simple finite graph G, general sum-connectivity index is defined for any real number α as χα(G) = 
, which generalises both the first Zagreb index and the ordinary sum-connectivity index. In this paper, we present some new bounds for the general sum-connectivity index. We also present relation between general sum-connectivity index and general Randić index.
References
A. Ali, M. Javaid, M. Matejić, I. Milovanović and E. Milovanović, “Some new bounds on the general sum-connectivity index”, Communications in Combinatorics and Optimization, vol. 5, no. 2, pp. 97-109, 2020.
B. Borovićanin, K.C. Das, B. Furtula and I. Gutman, “Bounds for Zagreb Indices”, MATCH Commun. Math. Comput. Chem., vol. 78, pp. 17-100, 2017.
Z. Chea and Z. Chen, “Lower and upper bounds of the forgotten topological index”, MATCH Commun. Math. Comput. Chem., vol. 76, pp. 635-648, 2016.
Z. Cvetkovski, Inequalities. Springer, Berlin, 2012.
T. Došlić, “Vertex-Weighted Wiener Polynomials for Composite Graphs”, Ars Math. Contemp., vol. 1, pp. 66-80, 2008.
I. Gutman and J. Tošović, “Testing the quality of molecular structure descriptors. Vertex-degree based topological indices”, J. Serb. Chem. Soc., vol. 78, pp. 805-810, 2013.
D. J. Klein, T. Došlić and D. Bonchev, “Vertex-weightings for distance moments and thorny graphs”, Discrete Appl. Math., vol. 155, pp. 2294-2302, 2007.
X. Li and I. Gutman, Mathematical Aspects of Randić-Type Molecular Structure Descriptors, University of Kragujevac, Kragujevac, 2006.
X. Li and J. Zheng, “A unified approach to the extremal trees for different indices”, MATCH Commun. Math. Comput. Chem., vol. 54, pp. 195-208, 2005.
B. Liu and I. Gutman, “On general Randić indices”, MATCH Commun. Math. Comput. Chem., vol. 58, pp. 147-154, 2007.
M. Matejić, I. Milovanović and E. Milovanović, “Some Inequalities for General Sum-Connectivity Index”, J. Appl. Math. and Informatics, vol. 38, pp. 189-200, 2020.
I. Milovanović, E. Milovanović and M. Matejić, “Some Inequalities for General Sum-Connectivity Index”, MATCH Commun. Math. Comput. Chem., vol. 79, pp. 477-489, 2018.
S. Nikolić, G. Kovačević, A. Miličević and N. Trinajstić, “The Zagreb Indices 30 Years After”, Croat. Chem. Acta, vol. 76, pp. 113-124, 2003.
C. Phanjoubam, S. M. Mawiong and A. M. Buhphang, “On general Sombor index of graphs”, Asian-European Journal of Mathematics, Art ID. 2350052. https://doi.org/10.1142/S1793557123500523
S. Stankov, M. Matejić, I. Milovanović, E. Milovanović and S. Altindağ, “Some new bounds on the first Zagreb index”, Electron. J. Math., vol. 1, pp. 101-107, 2021.
R. Todeschini and V. Consonni, Handbook of Molecular Descriptors, Wiley, Weinheim, 2000.
H. Wiener, “Structural determination of paraffin boiling points”, J. Am. Chem. Soc., vol. 69, pp. 17-20, 1947.
B. Zhou and W. Luo, “A note on general Randić indices”, MATCH Commun. Math. Comput. Chem., vol. 62, pp. 155-162, 2009.
B. Zhou and N. Trinajstić, “On a novel connectivity index”, J. Math. Chem., vol. 46, pp. 1252-1270, 2009.
B. Zhou and N. Trinajstić, On general sum-connectivity index, J. Math. Chem., vol. 47, pp. 210-218, 2010.
B. Zhou and D. Vukičević, “On general Randić and general zeroth-order Randić indices”, MATCH Commun. Math. Comput. Chem., vol. 62, pp. 189-196, 2009.
Published
How to Cite
Issue
Section
Copyright (c) 2023 Chinglensana Phanjoubam, Sainkupar Mawiong, Ardeline Buhphang
This work is licensed under a Creative Commons Attribution 4.0 International License.
-
Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
