Pebbling number

Pebbling number --- фишечное число.

The pebbling number of a graph [math]\displaystyle{ G }[/math], [math]\displaystyle{ f(G) }[/math], is the least [math]\displaystyle{ m }[/math] such that, however [math]\displaystyle{ m }[/math] are placed on the vertices of [math]\displaystyle{ G }[/math], we can move a pebble to any vertex by a sequence of moves, each move taking two pebbles off one vertex and placing one on an adjacent vertex.

We say a graph satisfies the 2-pebbling property, if two pebbles can be moved to any specified vertex, when the total starting number of pebbles is [math]\displaystyle{ 2f(G) - q + 1 }[/math], where [math]\displaystyle{ q }[/math] is the number of vertices with at least one pebble.

A graph [math]\displaystyle{ G }[/math] without the 2-pebbling property is called a Lemke graph.