Sombor Energy of a Graph with Self–Loops
This study aims to extend the notion of degree-based topological index, associated adjacency-type matrix and its energy from a simple graph to a graph with self-loops. Let GS be a graph with k self-loops obtained from a simple graph G, we define Sombor index for GS as (Figure Presented) where S ⊆ V(G) having self-loop to each of its vertices in S. In addition we investigate some fundamental properties of Sombor eigenvalues, McClelland and Koolen-Moulton-type bound for Sombor energy of GS. Also explores the correlation between Sombor energy of GS and the total π−electron energies associated with the corresponding hetero-molecular systems.
Anchan, Deekshitha Vivek; D’Souza, Sabitha; Gowtham, H. J.; and Bhat, Pradeep G., "Sombor Energy of a Graph with Self–Loops" (2023). Open Access archive. 6054.