2025/12/04 by Jasem Hamoud, Hamoud, Jasem, Duaa Abdullah +1
Computer Science · Mathematics · #05C05 #05C12 #05C20 #05C25 #05C35 #05C76 #68R10 #Commutative Algebra and Its Applications #FOS: Mathematics #G.2.2 #General Mathematics (math.GM) #Graph theory and applications #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2512.06023
openalex created_date 2025/12/04 · openalex publication_date 2025/12/04 · openalex updated_date 2026/07/28
In this paper, we presents novel and sharp bounds on the Albertson index of trees, revealing deep connections between degree sequences and graph irregularity where the Albertson index of Caterpillar tree satisfy irr(G)=( dn - 1 )2 + ( d1 - 1 )2 + ∑i = 2n - 1 ( di - 1 )( di - 2 ) +∑i=1n-1|di-di+1|. We derive powerful inequalities that precisely characterize the minimum and maximum values of the Albertson index, incorporating intricate dependencies on vertex degrees, edge counts, and the average of elements in degree sequence \mathscrD=(d1,d2,…,dn) where dn\geqslant dn-1\geqslant …\geqslant d2\geqslant d1. Our results not only improve existing extremal bounds but also uncover striking relationships between the structure of trees and their irregularity measurements. These advances open new avenues for the analysis of graph irregularity and contribute essential tools for the study of degree-based topological indices in combinatorial graph theory.