On the σt-irregularity and the inverse irregularity problem

Darko Dimitrov and Dragan Stevanović

Applied Mathematics and Computation, 2023, vol. 441, issue C

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 σt(G)=12∑v,w∈V(G)(dG(v)−dG(w))2, 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: Irregularity (of graph); Irregularity measure; Inverse irregularity problem (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:441:y:2023:i:c:s0096300322007779

DOI: 10.1016/j.amc.2022.127709

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