Exploring graph energies of k-copies of complete graph Kn with a common vertex
Resumen
In this study, we have calculated the energy, Seidel energy, and distance energy for k-copies of
the complete graph Kn, where the graphs share a single common vertex. Additionally, we derived expressions
for the Laplacian energy, Laplacian distance energy, and Laplacian Seidel energy for these graphs. To facilitate
these computations, we also developed a Python code that generates the corresponding energy values.
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Citas
1. D. Cvetkovi´c, I. Gutman, Applications of graph spectra, Math. Inst., Belgrade, (2009).
2. D. Cvetkovi´c, I. Gutman, Selected topics on applications of graph spectra, Math. Inst., Belgrade, (2011).
3. I. Gutman, The energy of a graph, Ber. Math-Statist. Sekt. Forschungsz. Graz 103, 1–22, (1978).
4. I. Gutman, O. E. Polansky, Mathematical concepts in organic chemistry, Springer, Berlin, (1986).
5. I. Gutman, The energy of a graph: old and new results, in: A. Betten, A. Kohnert, R. Laue, A. Wassermann (Eds.),
Algebraic Combinatorics and Applications, Springer, Berlin, pp. 196–211, (2001).
6. R. L. Graham, H. O. Pollak, On the addressing problem for loop switching, Bell Syst. Tech. J. 50, 2495–2519, (1971).
7. H. S. Ramane, D. S. Revankar, I. Gutman, S. B. Rao, B. D. Acharya, H. B. Walikar, Bounds for the distance energy
of a graph, Kragujevac J. Math. 31, 59–68, (2008).
8. G. Indulal, I. Gutman, A. Vijayakumar, On the distance energy of a graph, MATCH Commun. Math. Comput. Chem.
60, 461–472, (2008).
9. W. H. Haemers, Seidel switching and graph energy, MATCH Commun. Math. Comput. Chem. 68, 653–659, (2012).
10. I. Gutman, B. Zhou, Laplacian energy of a graph, Linear Algebra Appl. 414, 29–37, (2006).
11. F. Harary, Graph theory, Addison-Wesley Publ., (1969).
12. I. Gutman, B. Furtula, The total π-electron energy saga, Croat. Chem. Acta 90, 359–368, (2017).
13. I. Gutman, B. Furtula, Energies of graphs — survey, census, bibliography, Center Sci. Res., Kragujevac, (2019).
14. X. Li, Y. Shi, I. Gutman, Graph energy, Springer, New York, (2012).
2. D. Cvetkovi´c, I. Gutman, Selected topics on applications of graph spectra, Math. Inst., Belgrade, (2011).
3. I. Gutman, The energy of a graph, Ber. Math-Statist. Sekt. Forschungsz. Graz 103, 1–22, (1978).
4. I. Gutman, O. E. Polansky, Mathematical concepts in organic chemistry, Springer, Berlin, (1986).
5. I. Gutman, The energy of a graph: old and new results, in: A. Betten, A. Kohnert, R. Laue, A. Wassermann (Eds.),
Algebraic Combinatorics and Applications, Springer, Berlin, pp. 196–211, (2001).
6. R. L. Graham, H. O. Pollak, On the addressing problem for loop switching, Bell Syst. Tech. J. 50, 2495–2519, (1971).
7. H. S. Ramane, D. S. Revankar, I. Gutman, S. B. Rao, B. D. Acharya, H. B. Walikar, Bounds for the distance energy
of a graph, Kragujevac J. Math. 31, 59–68, (2008).
8. G. Indulal, I. Gutman, A. Vijayakumar, On the distance energy of a graph, MATCH Commun. Math. Comput. Chem.
60, 461–472, (2008).
9. W. H. Haemers, Seidel switching and graph energy, MATCH Commun. Math. Comput. Chem. 68, 653–659, (2012).
10. I. Gutman, B. Zhou, Laplacian energy of a graph, Linear Algebra Appl. 414, 29–37, (2006).
11. F. Harary, Graph theory, Addison-Wesley Publ., (1969).
12. I. Gutman, B. Furtula, The total π-electron energy saga, Croat. Chem. Acta 90, 359–368, (2017).
13. I. Gutman, B. Furtula, Energies of graphs — survey, census, bibliography, Center Sci. Res., Kragujevac, (2019).
14. X. Li, Y. Shi, I. Gutman, Graph energy, Springer, New York, (2012).
Publicado
2025-11-01
Número
Sección
Research Articles
Derechos de autor 2025 Boletim da Sociedade Paranaense de Matemática
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