A directed graph $G=(V,E)$ is called strongly biconnected if $G$ is strongly connected and the underlying graph of $G$ is biconnected. A strongly biconnected component of a strongly connected graph $G=(V,E)$ is a maximal vertex subset $L\subseteq V$ such that the induced subgraph on $L$ is strongly biconnected. Let $G=(V,E)$ be a strongly biconnected directed graph. A $2$-edge-biconnected block in $G$ is a maximal vertex subset $U\subseteq V$ such that for any two distict vertices $v,w \in U$ and for each edge $b\in E$, the vertices $v,w$ are in the same strongly biconnected components of $G\setminus\left\lbrace b\right\rbrace $. A $2$-strong-biconnected block in $G$ is a maximal vertex subset $U\subseteq V$ of size at least $2$ such that for every pair of distinct vertices $v,w\in U$ and for every vertex $z\in V\setminus\left\lbrace v,w \right\rbrace $, the vertices $v$ and $w$ are in the same strongly biconnected component of $G\setminus \left\lbrace v,w \right\rbrace $. In this paper we study $2$-edge-biconnected blocks and $2$-strong biconnected blocks.
翻译:G=(V,E) 指向 $G = (V,E) $, 如果$G$有强烈连接, 而基底的G$是双连接的。 强烈连接的G$(V,E) $(V,E) $(美元) 的强烈双连接部分是一个最大顶点子部分。 一个强烈连接的G$(V,E) $(G) 是一个强烈的双点点点点点点点。 一个强烈连接的G$(V,E) $(V,E) 是一个强烈的双点点点点点点部分。 一个强烈的双点点点部分是: 强烈连接的G=(V,E) $(V) $(V) 。 顶点是$(V) 美元(O) 的顶点部分: 美元(U) 美元(U/ sub) 美元(美元) 。