2021/07/12 by Zhen Lin, Ting Zhou, Lin, Zhen +3 · 1 citation
Chemistry · Computer Science · Mathematics · #05C05 #05C07 #05C09 #05C35 #Combinatorics (math.CO) #Computational Drug Discovery Methods #FOS: Mathematics #Free Radicals and Antioxidants #Graph theory and applications
paper · pdf · doi:10.48550/arxiv.2107.06145
openalex publication_date 2021/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce the general Albertson irregularity index of a connected graph G and define it as Ap(G) =(∑uv∈ E(G)|d(u)-d(v)|p)(1)/(p), where p is a positive real number and d(v) is the degree of the vertex v in G. The new index is not only generalization of the well-known Albertson irregularity index and σ-index, but also it is the Minkowski norm of the degree of vertex. We present lower and upper bounds on the general Albertson irregularity index. In addition, we study the extremal value on the general Albertson irregularity index for trees of given order. Finally, we give the calculation formula of the general Albertson index of generalized Bethe trees and Kragujevac trees.