Comparing Energy and Sombor Energy - An Empirical Study

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 E(G) is the sum of absolute values of the eigenvalues of the adjacency matrix of the graph G. Analogously, the Sombor energy ESO(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 ESO(G) and E(G) for various classes of (molecular) graphs, and establish the respective regularities. The correlation between ESO(G) and E(G) if found to be much more perplexed than earlier reported.

On the Spectral Radius and Sombor Energy of the Non-Commuting Graph for Dihedral Groups

“…In correlation studies for molecules containing hetero atoms and their total electron energy with a correlation, Gowtham & Swamy [8] stated that the Sombor energy values were highly correlated with their total electron energy with a correlation coefficient of 0.952. However, a different result was shown by [22] in which they presented a numerical approach for comparing the Sombor energy and the adjacency energy of graphs, and it is still an open problem for Mathematical proof.…”

“…The methodology consists of constructing the Sombor matrix of 𝛤 𝐺 , finding the eigenvalues and the spectrum of the respective matrix, analyzing 𝜌(𝛤 𝐺 ), computing the Sombor energy, and thus observing the relationship between 𝜌(𝛤 𝐺 ) and the Sombor energy of the respected 𝛤 𝐺 . We also investigate the hyperenergetic property of 𝛤 𝐺 and we compare the Sombor energy, 𝐸 𝑆 (𝛤 𝐺 ) and the (ordinary) energy 𝐸 𝐴 (𝛤 𝐺 ) as one of the cases to answer the claim in [22].…”

On Sombor Index and Graph Energy

“…After the introduction of Sombor index, within a short span of time, a lot of works on it have been done by many researchers [3][4][5][13][14][15][16]. Relating the Sombor index SO(G) of a graph G with the energy ε(G) of G is one such instance among the others.…”

Sombor Energy of a Graph with Self-Loops

“…For more details on this matter see Ref. [20] In this paper, hetero-molecular systems in Fig. 1, from Ref.…”