TARU PUBLICATIONS
Journal of Information and Optimization Sciences cover
Hybrid Ā·Peer-reviewedĀ·ISSN (Online): 2169-0103Ā·ISSN (Print): 0252-2667

WoS Ā JIF 2026 : 0.4 (Q4)

Powered by:Powered by

Monthly Journal: Publishes theoretical and applied research on topics in information and optimization sciences.

Issues up to 2022 co-published with and available at:Taylor & Francis
submissions@tarupublications.com
Open Access Research Article

On a new variant Sombor matrix and energy of total transformation graphs of regular graphs

* , , ,

* Corresponding author · click or hover a name for details

pp. 727–740Vol. 47Issue 2February 2026DOI: 10.47974/JIOS-2052XML
Received:
13 Jan 2025
Published Online:
23 Jan 2026
Article type:
Research Article
Language:
EN
Article no.:
JIOS-2052
Pages:
727–740

Abstract

In this study, we introduce a new variant of the Sombor matrix, denoted by š’©š’®o(ζ), associated with a simple graph ζ(n, e), where the (i, j)-entry for i ≠ j is equal to √(Ļ‚i2 + Ļ‚j2) and 0 in the either case, where Ļ‚i represents the degree of ith vertex. The Sombor energy Eš’©š’®o (ζ) represents the sum of the absolute values of the eigenvalues of the Sombor matrix. The spectrum and Eš’©š’®o (ζ) is obtained for total transformation graphs ζxyz of regular graphs. Also as an application, a set of 26 hetero atoms with total Ļ€-electron energy is analyzed, and a regression analysis is performed using Eš’©š’®o (ζ) for the hetero atoms. The linear regression model yields a correlation coefficient of r = 0.982.

Keywords

Subject Classifications

05C0705C50

References

[1] B. Basavanagoud and E. Chitra, ā€œDegree square sum energy of graphs,ā€ J. Math. Appl., vol. 6, pp. 193-205 (2018).
[2] B. Basavanagoud and S. Policepatil, ā€œCombined degree sum energy of graphs,ā€ Ann. Math. Comput. Sci., vol. 6, pp. 58-79 (2022).
[3] D. S. Revankar, J. B. Veeragoudar and M. M. Patil, ā€œOn the degree sum energy of total transformation graphs of regular graphs,ā€ J. Inf. Optim. Sci., vol. 44, pp. 217-229 (2023).
[4] F. Harary, Graph Theory. Reading, MA: Addison-Wesley (1969).
[5] G. Indulal, I. Gutman and A. Vijayakumar, ā€œOn distance energy of graphs,ā€ MATCH Commun. Math. Comput. Chem., vol. 60, pp. 461-472 (2008).
[6] I. Gutman and N. Trinajstic’, ā€œGraph theory and molecular orbitals. Total Ļ€-electron energy of alternate hydrocarbons,ā€ Chem. Phys. Lett., vol. 17, pp. 535-538 (1972).
[7] I. Gutman, ā€œThe energy of a graph,ā€ Ber. Math-Statist. Sekt. Forschungszentrum Graz., vol. 103, pp. 1-22 (1978).
[8] K. C. Das and S. Sorgun, ā€œOn Randic energy of graphs,ā€ MATCH Commun. Math. Comput. Chem., vol. 72, no. 1, pp. 227-238 (2014).
[9] H. S. Ramane, D. S. Revankar and J. B. Patil, ā€œBounds for the degree sum eigenvalue and degree sum energy of a graph,ā€ Int. J. Pure Appl. Math. Sci., vol. 6, no. 2, pp. 161-167 (2013).
[10] H. S. Ramane and S. S. Shinde. ā€œDegree exponent polynomial of graphs obtained by some graph operations’’, Electronic Notes in Discrete Mathematics, vol. 63, pp. 161-168 (2017).
[11] S. M. Hosamani and I. Gutman, ā€œZagreb indices of transformation graphs and total transformation graphs,ā€ Appl. Math. Comput., vol. 247, no. 15, pp. 1156-1160 (2014).
[12] J. B. Veeragoudar and B. S. Bhadre, ā€œFirst Zagreb index and coindex of the block-transformation graphs Gαβγ,ā€ J. Inf. Optim. Sci., vol. 42 no. 6, 1397-1408 (2021).
[13] S. R. Jog and J. R. Gurjar, ā€œDegree sum exponent distance energy of some graphs,ā€ J. Indones. Math. Soc., vol. 27, pp. 64-74 (2021).
[14] B. Wu and J. Meng, ā€œBasic properties of total transformation graphs,ā€ J. Math. Study, vol. 34, pp. 109-116 (2001).Ā 

Views: 169Downloads: 86Citations: 0