b-articulation points and b-bridges in strongly biconnected directed graphs

07/03/2020

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by   Raed Jaberi, et al.

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A directed graph G=(V,E) is called strongly biconnected if G is strongly connected and the underlying graph of G is biconnected. This class of directed graphs was first introduced by Wu and Grumbach. Let G=(V,E) be a strongly biconnected directed graph. An edge e∈ E is a b-bridge if the subgraph G∖{ e} =(V,E∖{ e}) is not strongly biconnected. A vertex w∈ V is a b-articulation point if G∖{ w} is not strongly biconnected, where G∖{ w} is the subgraph obtained from G by removing w. In this paper we study b-articulation points and b-bridges.