Nilpotent graphs over skew PBW extensions
Sebasti\'an Higuera, Armando Reyes
TL;DR
This paper studies the properties of nilpotent graphs over skew PBW extensions, providing bounds on diameter and invariance of girth, thus generalizing known results from skew polynomial rings.
Contribution
It introduces new bounds for the diameter and girth of nilpotent graphs over skew PBW extensions, extending previous work on skew polynomial rings.
Findings
Bounds established for the diameter of nilpotent graphs.
Girth of the nilpotent graph remains invariant under polynomial extensions.
Results generalize known properties from skew polynomial rings.
Abstract
We investigate the diameter and girth of the nilpotent graph for skew PBW extensions over -primal rings, generalizing similar results on skew polynomial rings. Under certain compatibility conditions, we establish bounds for the diameter of the nilpotent graph and prove invariance of the girth under polynomial extensions.
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Taxonomy
Topicsgraph theory and CDMA systems · Graph Labeling and Dimension Problems · Advanced Algebra and Logic