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MatchVolume 89, Issue 2, 2023, Pages 371-388

Irregularity of Graphs(Article)(Open Access)

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  • aDepartment of Mathematics, Mongolian National University of Education, Baga toiruu-14, Ulaanbaatar, Mongolia
  • bFaculty of Science, University of Kragujevac, Kragujevac, Serbia
  • cÓbuda University, Bécsiút, 96/B, Budapest, H-1034, Hungary

Abstract

The irregularity of a graph is the sum of the absolute values of the differences of degrees of pairs of adjacent vertices. The extremal graph with minimal irregularity among trees of order n with maximum degree ∆ and the second maximum degree ∆1 are determined, as well as unicyclic graphs of order n with girth g and maximum degree ∆. Lower and upper bounds are established on irregularity. Furthermore, the inverse problem for the irregularity of maximally irregular graphs is solved. © 2023 University of Kragujevac, Faculty of Science. All rights reserved.

  • ISSN: 03406253
  • Source Type: Journal
  • Original language: English
  • DOI: 10.46793/match.89-2.371D
  • Document Type: Article
  • Publisher: University of Kragujevac, Faculty of Science

  Horoldagva, B.; Department of Mathematics, Mongolian National University of Education, Baga toiruu-14, Ulaanbaatar, Mongolia;
© Copyright 2023 Elsevier B.V., All rights reserved.

Cited by 2 documents

Azari, M. , Dehgardi, N.
Some basic mathematical properties of the misbalance hadeg index of graphs
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Dehgardi, N. , Azari, M. , Shang, Y.
Lower bounds on trees and unicyclic graphs with respect to the misbalance rodeg index
(2025) Heliyon
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