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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