Nordhaus–Gaddum type results for graph irregularities

Yuede Ma, Shujuan Cao, Yongtang Shi, Matthias Dehmer and Chengyi Xia

Applied Mathematics and Computation, 2019, vol. 343, issue C, 268-272

Abstract: A graph whose vertices have the same degree is called regular. Otherwise, the graph is irregular. In fact, various measures of irregularity have been proposed and examined. For a given graph G=(V,E) with V={v1,v2,…,vn} and edge set E(G), di is the vertex degree where 1 ≤ i ≤ n. The irregularity of G is defined by irr(G)=∑vivj∈E(G)|di−dj|. A similar measure can be defined by irr2(G)=∑vivj∈E(G)(di−dj)2. The total irregularity of G is defined by irrt(G)=12∑vi,vj∈V(G)|di−dj|. The variance of the vertex degrees is defined var(G)=1n∑i=1ndi2−(2mn)2. In this paper, we present some Nordhaus–Gaddum type results for these measures and draw conclusions.

Keywords: Regular graph; Graph irregularity; Nordhaus–Gaddum; Degree; Zagreb index (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:343:y:2019:i:c:p:268-272

DOI: 10.1016/j.amc.2018.09.057

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