Abstract
Let D be a simple digraph with eigenvalues z1, z2, …, zn. The energy of D is defined as , where Re(zi) is the real part of the eigenvalue zi. In this paper, a lower bound for the spectral radius of D will be established based on the number of subgraphs
in D, improving some of the lower bounds that appear in the literature. Furthermore, this result allows us to obtain an upper bound for the energy of D.
Keywords:
Acknowledgements
We would like to thank the anonymous referees for the careful reading of our manuscript and for the invaluable comments. J. Rodríguez was supported by MINEDUC-UA project, code ANT-1899 and Funded by the Initiation Program in Research – Universidad de Antofagasta, INI-19-06.
Disclosure statement
No potential conflict of interest was reported by the author(s).