Irregularity Measure of Graphs. (20th March 2023)

• Record Type: Journal Article
• Authors: Ghalavand, Ali; Gutman, Ivan; Tavakoli, Mostafa
• Other Names: Ma Xuanlong Academic Editor.
• Is Part Of: Journal of mathematics. Volume 2023(2023)
• Publication Date: 2023-03-20
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals; 510
• DOI: 10.1155/2023/4891183
• Languages: English
• ISSNs: 2314-4629

Abstract

Abstract : A simple graph G is said to be regular if its vertices have the same number of neighbors. Otherwise, G is nonregular. So far, various formulas, such as the Albertson index, total Albertson index, and degree deviation, have been introduced to quantify the irregularity of a graph. In this paper, we present sharp lower bounds for these indices in terms of the order, size, maximum degree, minimum degree, and forgotten and Zagreb indices of the underlying graph. We also prove that if G has the minimum value of degree deviation, among all nonregular n, m -graphs, then Δ G − δ G = 1 .