On some properties of graph irregularity indices with a particular regard to the σ-index

Tamás Réti

Applied Mathematics and Computation, 2019, vol. 344-345, 107-115

Abstract: Some well-known graph irregularity indices of a connected graph G are investigated. Our study is focused mainly on the comparison of the Bell’s degree-variance (Var(G)) and the Collatz–Sinogowitz irregularity index (CS(G)) with the recently introduced σ(G) irregularity index. It is a degree-based topological invariant calculated as σ(G)=F(G)−2M2(G) where M2(G) is the second Zagreb index, F(G)=∑d3(v), and d(v) is the degree of the vertex v in G. By introducing the notion of the complete split-like graphs representing a broad subclass of bidegreed connected graphs, it is shown that for these graphs the equality σ(G)=n2Var(G) holds.

Keywords: Graph irregularity; Complete split graph; Stepwise irregular graph (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:344-345:y:2019:i::p:107-115

DOI: 10.1016/j.amc.2018.10.010

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