A note on the energy of graphs with self-loops
Résumé
In this paper, we compute the spectra of some extended (bipartite) double graphs with self-loops and compare their energies. We also give a method to construct cospectral graphs with self loops.
Téléchargements
Références
S. Akbari, H. A. Menderj, M. H. Ang, J. Lim, Z . C. Ng, Some Results on Spectrum and Energy of Graphs with Loops, Bull. Malays. Math. Sci. Soc. 46 (2023), Art. No. 94.
J. Day, W. So, Singular value inequality and graph energy change, Electron. J. Linear Algebra, 16 (2007) 291–299.
I. Gutman, I. Redzepovic, B. Furtula, A. M. Sahal, Energy of graphs with self-loops, MATCH Commun. Math. Comput. Chem. 87 (2021) 645–652.
R. Horn and C. Johnson, Matrix Analysis, Cambridge University Press, Cambridge, 1989.
I. Jovanovi´c, E. Zogic, E. Glogi´c, On the conjecture related to the energy of graphs with self-loops, MATCH Commun. Math. Comput. Chem. 89 (2023), 479–488.
J. Liu, Y. Chen, D. Dimitrov, J. Chen, New Bounds on the Energy of Graphs with Self-Loops, MATCH Commun. Math. Comput. Chem, 91 (2024), 779-796.
A. Mandal, S. M. A. Nayeem, On Bounds of Energy of a Graph with Self-Loops. MATCH Commun. Math. Comput. Chem, 92 (2024), 703–727.
K. M. Popat, K. R. Shingal, Some new results on energy of graphs with self loops, Journal Math. Chem. 61 (2023), 1462–1469
K. M. Popat, K. R. Shingala, On Equienergetic Graphs and Graph Energy of Some Standard Graphs with Self loops, preprint, doi.org/10.21203/rs.3.rs-2831568/v1.
U. Preetha P., M. Suresh, E. Bonyah, On the spectrum, energy and Laplacian energy of graphs with self-loops, Heliyon 9 (2023), e17001.
B. R. Rakshith, K. C. Das, B. J. Manjunatha, Y. Shang, Relations between ordinary energy and energy of a self-loop graph, Heliyon 10 (2024), e27756.
Copyright (c) 2025 Boletim da Sociedade Paranaense de Matemática
Ce travail est disponible sous la licence Creative Commons Attribution 4.0 International .
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
