More on betweenness-uniform graphs |
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Authors: | Jana Coroničová Hurajová Tomáš Madaras |
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Affiliation: | 1.Faculty of Business Economics with seat in Ko?ice,University of Economics in Bratislava,Ko?ice,Slovak Republic;2.Institute of Mathematics, Faculty of Sciences,University of P. J. ?afárik,Ko?ice,Slovak Republic |
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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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