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More on betweenness-uniform graphs

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Abstract

We study graphs whose vertices possess the same value of betweenness centrality (which is defined as the sum of relative numbers of shortest paths passing through a given vertex). Extending previously known results of S. Gago, J. Hurajová, T. Madaras (2013), we show that, apart of cycles, such graphs cannot contain 2-valent vertices and, moreover, are 3-connected if their diameter is 2. In addition, we prove that the betweenness uniformity is satisfied in a wide graph family of semi-symmetric graphs, which enables us to construct a variety of nontrivial cubic betweenness-uniform graphs.

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Authors and Affiliations

  1. Faculty of Business Economics with seat in Košice, University of Economics in Bratislava, Tajovského 13, 041 30, Košice, Slovak Republic

    Jana Coroničová Hurajová

  2. Institute of Mathematics, Faculty of Sciences, University of P. J. Šafárik, Jesenná 5, 040 01, Košice, Slovak Republic

    Tomáš Madaras

Authors
  1. Jana Coroničová Hurajová
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  2. Tomáš Madaras
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Correspondence to Jana Coroničová Hurajová.

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Coroničová Hurajová, J., Madaras, T. More on betweenness-uniform graphs. Czech Math J 68, 293–306 (2018). https://doi.org/10.21136/CMJ.2018.0087-16

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  • DOI: https://doi.org/10.21136/CMJ.2018.0087-16

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