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

Author

Listed:
  • Xu, Kexiang
  • Gu, Xiaoqian
  • Gutman, Ivan

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.

Suggested Citation

  • Xu, Kexiang & Gu, Xiaoqian & Gutman, Ivan, 2018. "Relations between total irregularity and non-self-centrality of graphs," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 461-468.
  • Handle: RePEc:eee:apmaco:v:337:y:2018:i:c:p:461-468
    DOI: 10.1016/j.amc.2018.05.058
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    Cited by:

    1. Miklavič, Štefko & Šparl, Primož, 2021. "Distance-unbalancedness of graphs," Applied Mathematics and Computation, Elsevier, vol. 405(C).
    2. Tang, Zikai & Liu, Hechao & Luo, Huimin & Deng, Hanyuan, 2019. "Comparison between the non-self-centrality number and the total irregularity of graphs," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 332-337.

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