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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