Authors: Dimitrov, Darko
Stevanović, Dragan 
Affiliations: Mathematics 
Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: On the σt-irregularity and the inverse irregularity problem
Journal: Applied Mathematics and Computation
Volume: 441
First page: 127709
Issue Date: 15-Mar-2023
Rank: ~M21a
ISSN: 0096-3003
DOI: 10.1016/j.amc.2022.127709
Abstract: 
The σ-irregularity index is a natural variant of the well-established Albertson irregularity index. Here, we introduce an irregularity measure based on the σ-irregularity, which is a graph invariant with respect to a given degree sequence. We define it as [Formula presented], where dG(v) is the degree of a vertex v of G, and named it the total σ-irregularity. We characterize irregular graphs with minimal σt-irregularity. In addition, we consider the so-called inverse problem for the Albertson irregularity index, the total irregularity, and the σt-irregularity. For those irregularity measures, we study the problem for general graphs, trees, and c-cyclic graphs.
Keywords: Inverse irregularity problem | Irregularity (of graph) | Irregularity measure
Publisher: Elsevier

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