Bounds on the Reciprocal distance energy and Reciprocal distance Laplacian energies of a graph

ABSTRACT

Let G be a simple undirected connected graph. In this article, we find bounds on the Reciprocal Distance Energy, Reciprocal Distance Laplacian Energy and Reciprocal Distance signless Laplacian Energy. Furthermore, we characterized the graphs that attained some of those bounds.

Keywords:

• Energy graph
• Reciprocal distance energy
• Reciprocal distance Laplacian energy
• Reciprocal distance signless Laplacian energy
• Harary energy

2010 Mathematics Subject Classifications:

• 05c50
• 15A18
• 15A42

Acknowledgements

The authors would like to thank the referee for his/her constructive suggestions that improved the final version of this paper. M. Trigo thank the Program ‘Magister en Ciencias mención Matemática Aplicada’ of the Universidad de Antofagasta. Part of this research was conducted in ‘Coloquio de Matemática’ code CR-4486, of the Universidad de Antofagasta, Chile.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The authors thank the ‘Programa de Asistente de Investigación’ supported by the Vicerrectoría de Investigación, Innovación y Postgrado of the Universidad de Antofagasta and the MINEDUC-UA project code ANT1855-ANT1856-ANT1956.