On Sombor energy of graphs
https://doi.org/10.17586/2220-8054-2021-12-4-411-417
Abstract
The concept of Sombor index SO(G) was recently introduced by Gutman in the chemical graph theory. It is a vertex-degree-based topological index and is denoted by SO(G). This paper introduces a new matrix for a graph G, called the Sombor matrix, and defines a new variant of graph energy called Sombor energy ES(G) of a graph G. The striking feature of this new matrix is that it is related to well-known degree-based topological indices called forgotten indices. When ES(G) values of some molecules containing hetero atoms are correlated with their total πelectron energy, we got a good correlation with the correlation coefficient r = 0.976. Further, we found some bounds and characterizations on the largest eigenvalue of S(G) and Sombor energy of graphs.
About the Authors
K. J. Gowtham
Tumkur University, University College of Science
India
India
Dept. of Mathematics,
Tumakuru, Karnataka State, Pin 572 103.
Narahari Narasimha Swamy
Tumkur University, University College of Science
India
India
Dept. of Mathematics,
Tumakuru, Karnataka State, Pin 572 103.
References
1. Boregowda H.S., Jummannaver R.B. Neighbors degree sum energy of graphs. J. Appl. Math. Comput., 2021, https://doi.org/10.1007/s12190020-01480-y.
2. Gutman I., Trinajstic N. Graph theory and molecular orbitals. Total´ π-electron energy of alternant hydrocarbons. Chem. Phys. Lett., 1972, 17, P. 535–538.
3. Jafari Rad N., Jahanbani A., Gutman I. Zagreb Energy and Zagreb Estrada Index of Graphs. MATCH Commun. Math. Comput. Chem., 2018, 79, P. 371–386.
4. Rajendra P., Randic. Color Energy of a Graph.´ Int. Journal of Computer Applications, 2017, 171, P. 1–5.
5. Aouchiche M., Hansen P. Distance spectra of graphs: a survey. Linear Algebra Appl., 2014, 458, P. 301–386.
6. Brouwer A., Haemers W. Spectra of Graphs, Springer, Berlin, 2012.
7. Mohar B. The Laplacian spectrum of graphs. In: Alavi, Y., Chartrand, G., Ollermann, O.R., Schwenk, A.J. (eds.) Graph Theory, Combinatorics and Applications, Wiley, New-York, 1991, 2, P. 871–898.
8. Ramane H.S., Jummannaver R.B., Gutman I. Seidel Laplacian energy of graphs. Int. J. Appl. Graph. Theory, 2017, 2, P. 74–82.
9. Cvetkovic D., Rowlinson P., Simi´ c S.K. Eigenvalue bounds for the signless Laplacian.´ Publ. Inst. Math. (Beograd), 2007, 81, P. 11–27.
10. Ramane H.S., Gutman I., Patil J.B., Jummannaver R.B. Seidel signless Laplacian energy of graphs. Math. Interdiscip. Res., 2017, 2, P. 181– 192.
11. Ramane H.S., Revankar D.S., Patil J.B. Bounds for the degree sum eigenvalues and degree sum energy of a graph. Int. J. Pure Appl. Math. Sci., 2013, 6, P. 161–167.
12. Das K.C., Trinajstic N. Comparison between first geometric–arithmetic index and atom–bond connectivity index.´ Chem. Phys. Lett., 2010, 497, P. 149–151.
13. Graovac A., Gutman I., Trinajstic N. Total´ π-Electron Energy. In: Toplogical Approach to the Chemistry of Conjugated Molecules, 1977, 4, P. 48–78.
14. Gutman I. Degree-based topological indices. Croat. Chem. Acta, 2013, 86, P. 351–361.
15. Gutman I. Geometric approach to degree-based topological indices: Sombor indices. MATCH Commun. Math. Comput. Chem., 2021, 86, P. 11–16.
16. Das K.C., Cevik A.S., Cangul I.N., Shang Y. On Sombor Index. Symmetry, 2021, 13, 140.
17. Cruz R., Gutman I., Rada J. Sombor index of chemical graphs. Applied Mathematics and Computation, Elsevier, 2021, 399, 126018.
18. Deng H., Tang Z., Wu R. Molecular trees with extremal values of Sombor indices. Int. J. Quantum. Chem., 2021, 121 (11), e26622.
19. Gutman I. Some basic properties of Sombor indices. Open J. Discret. Appl. Math., 2021, 4, P. 1–3.
20. Horoldagva B., Xu C. On Sombor index of graphs. MATCH Commun. Math. Comput. Chem., 2021, 86, P. 703–713.
21. Kulli V.R., Gutman I. Computation of Sombor Indices of Certain Networks. Int. Journal of Applied Chemistry, 2021, 8, P. 1–5.
22. Liu H., You L., Tang Z., Liu J.B. On the reduced Sombor index and its applications. MATCH Commun. Math. Comput. Chem., 2021, 86, P. 729–753.
23. Milovanovic I., Milovanovi´ c E., Mateji´ c M. On some mathematical properties of Sombor indices.´ Bull. Int. Math. Virtual Inst., 2021, 11, P. 341–353.
24. Reti T., Dosli´ c T., Ali A. On the Sombor index of graphs.´ Contrib. Math., 2021, 3, P. 11–18.
25. Wang Zh., Mao Y., Li Y., Furtula B. On relations between Sombor and other degree-based indices. J. Appl. Math. Comput., 2021, doi:10.1007/s12190-021-01516-x.
26. Redzepoviˇ c I. Chemical applicability of Sombor indices.´ J. Serb. Chem. Soc., 2021, 86 (5), P. 445–457.
27. Furtula B., Gutman I. A forgotten topological index. J. Math. Chem., 2015, 53, P. 1184–1190.
28. Ramachandran K.I., Deepa G., Namboori K. Computational Chemistry and Molecular Modelling: Principles and Applications. Springer, Berlin, 2008.
29. Yates K. Huckel Molecular Orbital Theory. Academic Press, New York, 1978.
30. Coulson C.A., Streitwieser J. Dictionary of π-Electron Calculations. Freeman, San Francisco, 1965.
Review
For citations:
Gowtham K.J., Swamy N.N. On Sombor energy of graphs. Nanosystems: Physics, Chemistry, Mathematics. 2021;12(4):411-417. https://doi.org/10.17586/2220-8054-2021-12-4-411-417
Views:
7
Email this article 