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Article Title
Abstract
The \emph{betweenness centality} of an edge $e$ is, summed over all $u,v\in V(G)$, the ratio of the number of shortest $u,v$-paths in $G$ containing $e$ to the number of shortest $u,v$-paths in $G$. Graphs whose vertices all have the same edge betweenness centrality are called \emph{edge betweeness-uniform}. It was recently shown by Madaras, Hurajová, Newman, Miranda, Fl\'{o}rez, and Narayan that of the over 11.7 million graphs with ten vertices or fewer, only four graphs are edge betweenness-uniform but not edge-transitive.In this paper we present new results involving properties of betweenness-uniform graphs.
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Recommended Citation
Coroničová Hurajová, Jana; Madaras, Tomas; and Narayan, Darren A.
(2022)
"Characterizing Edge Betweenness-Uniform graphs,"
Theory and Applications of Graphs: Vol. 9:
Iss.
1, Article 5.
DOI: 10.20429/tag.2022.090105
Available at:
https://digitalcommons.georgiasouthern.edu/tag/vol9/iss1/5