On Sombor coindex of graphs

TL;DR

This paper introduces the Sombor coindex, a new graph topological index based on non-adjacent vertex pairs, exploring its properties, relationships, bounds, and applications to chemical graphs.

Contribution

The paper defines the Sombor coindex, analyzes its properties and relations to existing indices, and computes bounds and applications to chemical graphs.

Findings

Sombor coindex relates to Sombor and Zagreb indices.

Bounds for Sombor coindex under graph operations are established.

Application to chemical graphs demonstrates practical relevance.

Abstract

Motivated by the recently introduced topological index, the Somber index, we define a new topological index of a graph in this paper, we call it Sombor coindex. The Sombor coindex is defined by considering analogous contributions from the pairs of non-adjacent vertices, capturing, thus, and quantifying a possible influence of remote pairs of vertices. We give several properties of the Somber coindex and its relations to the Sombor index, the Zagreb (co)indices, forgotten coindex and other important graph parameters. We also compute the bounds of the Somber coindex of some graph operations and compute the Sombor coindex for some chemical graphs as an application.