Year: 2026
Type: article
Abstract: where the sum is over all edges of G.In 2005, Hansen and Mélot proved an upper bound on the irregularity of a graph on n vertices and m edges that is attained for all feasible values, and characterized the extremal graphs.We give a much shorter proof of this result, and discuss some of its implications.Denoting the extremal graphs as near k-star graphs, we show that they sometimes occur as extremal graphs for related problems on sigma irregularity and first Zagreb index.
Source: Discrete Mathematics Letters
Author: Allan Bickle
Institution: Purdue University West Lafayette
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7223910062