On the non-commuting graph associated to a finite-dimensional Lie algebra

TL;DR

This paper introduces the non-commuting graph of a finite-dimensional Lie algebra, analyzing its fundamental properties like connectivity, diameter, girth, and conditions for planarity and isomorphism.

Contribution

It provides a systematic study of the graph-theoretic properties of the non-commuting graph associated with finite-dimensional Lie algebras, including new insights into its structural characteristics.

Findings

The non-commuting graph is connected with specific diameter and girth.

Conditions for planarity and outer planarity are established.

Isomorphism criteria between such graphs are discussed.

Abstract

In this paper, we define the non-commuting graph associated to a Lie algebra L and obtain some basic graph properties such as connectivity, diameter, girth, Hamiltonian and Eulerian. Moreover, planarity, outer planarity and isomorphism between two such graphs are also discussed in the paper.