Center vertex

Center vertex --- центральная вершина.

A vertex $v$ in a connected graph $G$ is called a center (central) vertex if $e(v) = rad(G)$. A subgraph induced by central vertices of $G$ is called the center $C(G)$ of $G$. It was proved that the center of every graph $H$ is contained in a block (a maximal 2-connected subgraph) of $H$.