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Title:
Comparing Energy and Sombor Energy - An Empirical Study
Authors:
Izudin Redžepović, Ivan Gutman
doi:
Volume
88
Issue
1
Year
2022
Pages
133-140
Abstract The Sombor index is a recently invented vertex-degree-based topological index, to which a matrix - called Sombor matrix - is associated in a natural manner. The graph energy \(\mathcal E(G)\) is the sum of absolute values of the eigenvalues of the adjacency matrix of the graph \(G\). Analogously, the Sombor energy \(\mathcal E_{SO}(G)\) is the sum of absolute values of the eigenvalues of the Sombor matrix. In this paper, we present computational results on the relations between \(\mathcal E_{SO}(G)\) and \(\mathcal E(G)\) for various classes of (molecular) graphs, and establish the respective regularities. The correlation between \(\mathcal E_{SO}(G)\) and \(\mathcal E(G)\) if found to be much more perplexed than earlier reported.

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