Basically, I am looking for a (well-defined) term for some "borderline" vertexes interconnecting other vertices in and outside of a given connected component.
More specifically, given directed graph $G = (V_G, E_G)$ and (strongly) connected component $C = (V_C, E_C)$, how do people refer to such vertices $x$, where,
- $x \in V_C$;
- $\exists\ v \in V_G \setminus V_C$ such that $(x, v) \in E_G \setminus E_C$;
My friends have suggested names such as gateway vertex and border vertex. But I feel obliged to make sure we are not reinventing something well-known / well-defined.
It would be helpful if someone can help identify an equivalent (or likewise) definition of this concept in the literature. Thanks a lot.
Please note that -- unlike the well-defined concept of cut vertex -- the concept of borderline vertex (or whatever it should be called) is with respect to a specific given component, not the entire graph.