A Study on the Energy of Graphs and Its Applications

Abstract

In this paper, we dealt with two very well-known eigenvalue-based molecular descriptors such as the energy of graph $(\mathcal{E}(G))$ and Estrada index $(EE(G)).$ We test their predictive potential of some physicochemical properties of polycyclic aromatic hydrocarbons using a data set of benzenoid hydrocarbons. We stabilized a relation of these two indices with some well-known degree-based topological indices such as the first Zagreb index, second Zagreb index, F-index, Randić index, Reciprocal Randić index, Atom bond connectivity index, sum-connectivity index, Geometric-arithmetic, Harmonic index, symmetric division deg index, and redefined Zagreb index.

Keywords:

• Energy of graph ($\mathcal{E}(G)$)
• Estrada index (EE(G))
• Degree-based topological indices

MSC (2010):

• Primary: 05C35
• secondary: 05C07
• 05C40

Acknowledgements

We would like to thank the anonymous reviewers for their careful reading of our manuscript and their many insightful comments and suggestions to improve the manuscript.

Availability of data and software

The experimental data for benzenoid hydrocarbons were taken from 22. MATLAB was used for computing eigenvalues of the underlying molecular graphs, and MS Excel was used for statistical analyses.

Authors’ contributions

SK – Writing-Verified the results, Reviewed and Editing; PS – Conceptualization, Writing- Original draft preparation; AP – Writing-Reviewed and Editing, Supervision, Validation.

Disclosure statement

The authors declare that they have no competing interests.