Some observations on sombor coindex of graphs

Document Type : Short notes

Authors

Faculty of Electronic Engineering, University of Niš, Niš, Serbia

Abstract

Let $G=(V,E)$, $V=\left\{ v_{1},v_{2},\ldots ,v_{n}\right\}$, be a simple graph of order $n$ and size $m$, without isolated vertices. The Sombor coindex of a graph $G$ is defined as  $\overline{SO}(G)=\sum_{i\nsim j}\sqrt{d_i^2+d_j^2}$ , where $d_i= d(v_i)$ is a degree of vertex $v_i$, $i=1,2,\ldots , n$. In this paper we investigate a relationship  between  Sombor coindex and a number of other topological coindices. 

Keywords

Main Subjects

References

[1] M.O. Albertson, The irregularity of a graph, Ars Combin. 46 (1997), 219–225.
[2] A.R. Ashrafi, T. Došlić, and A. Hamzeh, The Zagreb coindices of graph operations, Discrete Appl. Math. 158 (2010), no. 15, 1571–1578.  https://doi.org/10.1016/j.dam.2010.05.017
[3] B. Bollobás and P. Erdös, Graphs of extremal weights, Ars Combin. 50 (1998), 225–233.
[4] M. Cavers, S. Fallat, and S. Kirkland, On the normalized Laplacian energy and general Randić index R−1 of graphs, Lin. Algebra Appl. 433 (2010), no. 1, 172–190.  https://doi.org/10.1016/j.laa.2010.02.002
[5] K.C. Das and I. Gutman, Some properties of the second Zagreb index, MATCH Commun. Math. Comput. Chem. 52 (2004), no. 1, 103–112.
[6] T. Došlić, Vertex-weighted Wiener polynomials for composite graphs, Ars Math. Contemp. 1 (2008), no. 1, 66–80.  https://doi.org/10.26493/1855-3974.15.895
[7] T. Došlić, B. Furtula, A. Graovac, I. Gutman, S. Moradi, and Z. Yarahmadi, On vertex-degree-based molecular structure descriptors, MATCH Commun. Math.  Comput. Chem. 66 (2011), no. 2, 613–626.
[8] S. Fajtlowicz, On conjectures of Graffiti-II, Congr. Numer. 60 (1987), 187–197.
[9] S. Filipovski, Relations between Sombor index and some degree-based topological indices, Iranian J. Math. Chem. 12 (2021), no. 1, 19–26.  https://doi.org/10.22052/ijmc.2021.240385.1533
[10] B. Furtula and I. Gutman, A forgotten topological index, J. Math. Chem. 53 (2015), no. 4, 1184–1190.  https://doi.org/10.1007/s10910-015-0480-z
[11] I. Gutman, Degree-based topological indices, Croat. Chem. Acta 86 (2013), no. 4, 351–361.  http://dx.doi.org/10.5562/cca2294
[12] I. Gutman, Geometric approach to degree-based topological indices: Sombor indices, MATCH Commun. Math. Comput. Chem. 86 (2021), no. 1, 11–16.
[13] I. Gutman, Some basic properties of Sombor indices, Open J. Discrete Appl. Math. 4 (2021), no. 1, 1–3.  https://doi.org/10.30538/psrp-odam2021.0047
[14] I. Gutman, B. Furtula, and C. Elphick, Three new/old vertex-degree-based topological indices, MATCH Commun. Math. Comput. Chem. 72 (2014), no. 3, 617–632.
[15] I. Gutman, B. Ruščić, N. Trinajstić, and C.F. Wilcox Jr, Graph theory and molecular orbitals. XII. Acyclic polyenes, J. Chem. Phys. 62 (1975), no. 9, 3399–3405.  https://doi.org/10.1063/1.430994
[16] I. Gutman and N. Trinajstić, Graph theory and molecular orbitals. Total ϕ-electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972), no. 4, 535–538.  https://doi.org/10.1016/0009-2614(72)85099-1
[17] J.G. Kemeny and J.L. Snell, Finite Markov chains, Van Nostrand, Princeton, N.J., 1960.
[18] I. Milovanović, E. Milovanović, I. Gutman, and B. Furtula, Some inequalities for the forgotten topological index, Int. J. Appl. Graph Theory 1 (2017), no. 1, 1–15.
[19] I. Milovanović, E. Milovanović, and M. Matejić, On some mathematical properties of Sombor indices, Bull. Int. Math. Virtual Inst. 11 (2021), no. 2, 341–353.  https://doi.org/10.7251/BIMVI2102341M
[20] S. Nikolić, G. Kovačević, A. Miličević, and N. Trinajstić, The Zagreb indices 30 years after, Croat. Chem. Acta 76 (2003), no. 2, 113–124.
[21] K. Pattabiraman, A note on the symmetric division deg coindex of graphs, Electron. J. Math. 2 (2021), 37–43.  https://doi.org/10.47443/ejm.2021.0029
[22] C. Phanjoubam, S.M. Mawiong, and A.M. Buhphang, On Sombor coindex of graphs, Commun. Comb. Optim. 8 (2023), no. 3, 513–529.  https://doi.org/10.22049/cco.2022.27751.1343
[23] J.R. Platt, Influence of neighbor bonds on additive bond properties in paraffins, J. Chem. Phys. 15 (1947), no. 6, 419–420.  https://doi.org/10.1063/1.1746554
[24] J. Radon, Theorie und Anwendungen der absolut additiven Mengenfunktionen, Sitzungsber. Acad. Wissen. Wien 122 (1913), 1295–1438.
[25] M. Randić, Characterization of molecular branching, J. Amer. Chem. Soc. 97 (1975), no. 23, 6609–6615.  https://doi.org/10.1021/ja00856a001
[26] R. Todeschini and V. Consonni, Handbook of molecular descriptors, John Wiley & Sons, 2008.
[27] D. Vukičević, Bond additive modeling 2. Mathematical properties of max-min rodeg index, Croat. Chem. Acta 83 (2010), no. 3, 261–273.
[28] D. Vukičević and M. Gašperov, Bond additive modeling 1. Adriatic indices, Croat. Chem. Acta 83 (2010), no. 3, 243–260.
[29] H. Wiener, Structural determination of paraffin boiling points, J. Am. Chem. Soc. 69 (1947), no. 1, 17–20. https://doi.org/10.1021/ja01193a005
Communications in Combinatorics and Optimization
Volume 9, Issue 4
December 2024
Pages 813-825

Files

Share

How to cite

Statistics