(a,b)-Vertex pancyclic graph

[math]\displaystyle{ (a,b) }[/math]-Vertex pancyclic graph --- [math]\displaystyle{ (a,b) }[/math]-вершинно панциклический граф.

Let [math]\displaystyle{ a,b }[/math] be integers and [math]\displaystyle{ a \leq i \leq b }[/math]. [math]\displaystyle{ G }[/math] is called [math]\displaystyle{ (a,b) }[/math]-vertex pancyclic, if for any [math]\displaystyle{ u \in V }[/math] there exists a cycle containing [math]\displaystyle{ u }[/math] with [math]\displaystyle{ i }[/math] vertices. In particular, [math]\displaystyle{ G }[/math] is vertex pancyclic, if [math]\displaystyle{ a = 3 }[/math] and [math]\displaystyle{ b = |V| }[/math].