Extremizing antiregular graphs by modifying total σ-irregularity

Martin Knor, Riste Škrekovski, Slobodan Filipovski and Darko Dimitrov

Applied Mathematics and Computation, 2025, vol. 490, issue C

Abstract: The total σ-irregularity is given by σt(G)=∑{u,v}⊆V(G)(dG(u)−dG(v))2, where dG(z) indicates the degree of a vertex z within the graph G. It is known that the graphs maximizing σt-irregularity are split graphs with only a few distinct degrees. Since one might typically expect that graphs with as many distinct degrees as possible achieve maximum irregularity measures, we modify this invariant to σtf(n)(G)=∑{u,v}⊆V(G)|dG(u)−dG(v)|f(n), where n=|V(G)| and f(n)>0. We study under what conditions the above modification obtains its maximum for antiregular graphs. We consider general graphs, trees, and chemical graphs, and accompany our results with a few problems and conjectures.

Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:490:y:2025:i:c:s009630032400660x

DOI: 10.1016/j.amc.2024.129199

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