Center vertex

Center vertex --- центральная вершина.

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