$\sigma$-Irregularity of Trees with Prescribed Maximum Degree: A Majorization--Duality--Stability Framework

This paper establishes a unified majorization-duality-stability framework that characterizes trees with maximum $\sigma$-irregularity for any prescribed maximum degree $\Delta \ge 3$, providing closed-form solutions, duality relations, and stability bounds for the extremal structures.

Original authors: Jasem Hamoud, Duaa Abdullah