Pancentral graph

Pancentral graph --- панцентральный граф.

A graph [math]\displaystyle{ G }[/math] is called pan-unicentral if, given a vertex [math]\displaystyle{ v }[/math] in [math]\displaystyle{ G }[/math], there exists a spanning tree [math]\displaystyle{ T }[/math] such that [math]\displaystyle{ C(T) = \{v\} }[/math], where [math]\displaystyle{ C(T) }[/math] is the center of [math]\displaystyle{ T }[/math]. [math]\displaystyle{ G }[/math] is called pan-bicentral if, given adjacent vertices [math]\displaystyle{ u }[/math] and [math]\displaystyle{ v }[/math] in [math]\displaystyle{ G }[/math], there exists a spanning tree [math]\displaystyle{ T }[/math] such that [math]\displaystyle{ C(T) = \{u,v\} }[/math]. A graph [math]\displaystyle{ G }[/math] with both properties is called pancentral.