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Digraphs with large maximum Wiener index

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  • Knor, Martin
  • Škrekovski, Riste
  • Tepeh, Aleksandra

Abstract

Recently the concept of Wiener index was extended to digraphs which are not-necessarily strongly connected, and it was shown that some fundamental results extend naturally within this concept. This extension could be applicable in the topics of directed large networks, particularly because with this measure, one assigns finite values to the average distance and betweenness centrality of the nodes in a directed network. It is not hard to show that among digraphs on n vertices, the directed cycle C→n achieves the maximum Wiener index. Next, we investigate digraphs with the second maximum Wiener index. One can consider this problem in the realm of all digraphs or restricted to those obtained by directing undirected graphs, so called antisymmetric digraphs. In both situations, we obtain that such digraphs are constructed from C→n (n ≥ 6) by adding a single arc. We conclude the paper with consideration for possible further works.

Suggested Citation

  • Knor, Martin & Škrekovski, Riste & Tepeh, Aleksandra, 2016. "Digraphs with large maximum Wiener index," Applied Mathematics and Computation, Elsevier, vol. 284(C), pages 260-267.
    • Handle: RePEc:eee:apmaco:v:284:y:2016:i:c:p:260-267
    DOI: 10.1016/j.amc.2016.03.007
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    References listed on IDEAS

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    1. Knor, Martin & Škrekovski, Riste & Tepeh, Aleksandra, 2016. "Some remarks on Wiener index of oriented graphs," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 631-636.
    2. Cao, Shujuan & Dehmer, Matthias, 2015. "Degree-based entropies of networks revisited," Applied Mathematics and Computation, Elsevier, vol. 261(C), pages 141-147.
    3. Dehmer, Matthias & Emmert-Streib, Frank & Shi, Yongtang, 2015. "Graph distance measures based on topological indices revisited," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 623-633.
    4. Knor, Martin & Škrekovski, Riste & Tepeh, Aleksandra, 2015. "An inequality between the edge-Wiener index and the Wiener index of a graph," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 714-721.
    5. Li, Xueliang & Qin, Zhongmei & Wei, Meiqin & Gutman, Ivan & Dehmer, Matthias, 2015. "Novel inequalities for generalized graph entropies – Graph energies and topological indices," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 470-479.
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    Cited by:

    1. Ji, Shengjin & Liu, Mengmeng & Wu, Jianliang, 2018. "A lower bound of revised Szeged index of bicyclic graphs," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 480-487.
    2. Hriňáková, Katarína & Knor, Martin & Škrekovski, Riste, 2019. "An inequality between variable wiener index and variable szeged index," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.

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