Relations between total irregularity and non-self-centrality of graphs

Kexiang Xu, Xiaoqian Gu and Ivan Gutman

Applied Mathematics and Computation, 2018, vol. 337, issue C, 461-468

Abstract: For a connected graph G, with degG(vi) and ɛG(vi) denoting the degree and eccentricity of the vertex vi, the non-self-centrality number and the total irregularity of G are defined as N(G)=∑|ɛG(vj)−ɛG(vi)| and irrt(G)=∑|degG(vj)−degG(vi)|, with summations embracing all pairs of vertices. In this paper, we focus on relations between these two structural invariants. It is proved that irrt(G) > N(G) holds for almost all graphs. Some graphs are constructed for which N(G)=irrt(G). Moreover, we prove that N(T) > irrt(T) for any tree T of order n ≥ 15 with diameter d ≥ 2n/3 and maximum degree 3.

Keywords: Degree (of vertex); Eccentricity (of vertex); Total irregularity; Non-self-centrality number (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:337:y:2018:i:c:p:461-468

DOI: 10.1016/j.amc.2018.05.058

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