The Commuting Graphs of Certain Solvable Lie Algebras
Hieu V. Ha, Vu A. Le, Tuan A. Nguyen, Tuyen T. M. Nguyen, Hoa D. Quang

TL;DR
This paper characterizes the structure of commuting graphs for solvable Lie algebras of dimension up to 4, revealing their connected components and graph properties.
Contribution
It provides a detailed description of the connected components of commuting graphs for low-dimensional solvable Lie algebras, a previously less explored area.
Findings
Connected components of commuting graphs are classified for dimension ≤ 4.
The structure of these graphs depends on the algebra's center and Lie bracket relations.
Results facilitate understanding of algebraic and graph-theoretic properties of solvable Lie algebras.
Abstract
Let be the center of a Lie algebra with Lie bracket . %We then define The commuting graph of is then defined by the simple undirected graph in which the vertex set is and the set of edges . The main purpose of this paper is to accurately describe the connected components of the commuting graph of solvable Lie algebras of dimension at most 4.
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Taxonomy
TopicsAdvanced Topics in Algebra · Finite Group Theory Research · Algebraic structures and combinatorial models
