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Submitted
May 15, 2021
Accepted
November 28, 2022
Published
November 29, 2022
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Abstract

This paper defines and computes the degree square subtraction matrix, its characteristic polynomial and spectra in terms of the first Zagreb Index. We explore its bounds for spectral radius and energy.

Keywords

DSS(G) characteristic polynomial Of DSS(G) DSS-Spectra DSS-Eigenvalues DSSE(G).

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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

How to Cite
Macha, J. S., & Shinde, S. N. (2022). Degree Square Subtraction Spectra and Energy. Journal of the Indonesian Mathematical Society, 28(3), 259–271. https://doi.org/10.22342/jims.28.3.1007.259-271
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References

  1. Abdussakir, Sudarman, Jauhari, M. N., and Ali, F., Survey on topological indices and graphs associated with a commutative ring, Journal of Physics: Conference Series, 1562 (2020), 012008.
  2. Aouchiche, M. and Hansen, P., Distance spectra of graphs: A survey, Linear Algebra Appl., 458 (2014), 301-386.
  3. Barnard, S. and Child, J. M., Higher Algebra, Macmillan, New York, 1959.
  4. Basavanagoud B. E. Chitra, Degree square sum polynomial of some special graphs, Int. J. Math. And Appl., 6(2B)(2018), 193-205
  5. Borovianin, B., Das, K., Furtula, B., and Gutman, I., Bounds for Zagreb indices, Match Communications in Mathematical and in Computer Chemistry, 78 (2017), 17-100.
  6. Cioab, S. M., Sums of powers of the degrees of a graph, Discrete mathematics, 306 (2006), 1959-1964.
  7. Cvetkovic, D., Doob, M., and Sachs, H., Spectra of Graphs: Theory and Applications, Academic Press, New York, 1980.
  8. Fath-Tabar, G. H. and Ashrafi, A. R., Some remarks on Laplacian eigenvalues and Laplacian energy of graphs, Math. Commun., 15(2010), 443-451.
  9. Gutman, I. and Polansky, O. E., Mathematical Concepts in Organic Chemistry, SpringerVerlag, Berlin (1986).
  10. Gutman, I., The energy of a graph, Ber. Math. Stat. Sekt. Forschungsz. Graz, 103 (1978), 1-22.
  11. Gutman, I. and Trinajstic, N., Graph theory and molecular orbitals, Total π-electron energy of alternant hydrocarbons, Chem. Phys. Lett., 17(1972) 535-538 .
  12. Gutman, I. and Zhou, B., Laplacian energy of a graph, Linear Algebra Appl., 414(2006), 29-37.
  13. Harary, F., Graph Theory, Addison-Wesley, Reading, Mass, 1969.
  14. Indulal, G., Gutman, I., and Vijayakumar, A., On distance energy of graphs, MATCH Commun. Math. Comput. Chem., 60(2008), pp. 461-472.
  15. Mohar, B., The Laplacian spectrum of graphs, (Y. Alavi, G. Chartrand, O. R. Oellermann, and A. J. Schwenk, eds.), Graph Theory, Combin. Appl, 2 (1991), 871-898.
  16. Ramane, H. S., Nandeesh, K. C., Gudodagi, G. A., and Zhou, B., Degree subtraction eigenvalues and energy of graphs, Computer Science Journal of Moldova, 26, no.2(77), (2018).
  17. Shinde, S. S. and Macha, J., Degree Exponent Subtraction Energy, Advances in Mathematics: Scientific Journal, 9 (2020), 9137-9148.
  18. Shinde, S. S., Ramane, H. S., Gudimani, S. B., and Swamy, N., Degree sum adjacency polynomial of standard graphs and graph operations, Electronic journal of graph theory and applications, Accepted.
  19. Steele, J. M., The CauchySchwarz Master Class, An Introduction to the Art of Mathematical Inequalities, 2004