Sombor Energy of a Graph with Self–Loops

Authors

Deekshitha Vivek Anchan, Manipal Institute of Technology
Sabitha D’Souza, Manipal Institute of Technology
H. J. Gowtham, Manipal Institute of Technology
Pradeep G. Bhat, Manipal Institute of Technology

Document Type

Article

Publication Title

Match

Abstract

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.

First Page

733

Last Page

786

DOI

10.46793/match.90-3.773A

Publication Date

1-1-2023

Recommended Citation

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.
https://impressions.manipal.edu/open-access-archive/6054