a k-leaf power, fixed k if there is a tree T whose leaves correspond to the vertices of G in such a way that two vertices are adjacent in G precisely when their distance in T is at most k
a triple ( V ( G ), E ( G ), a G ) where V ( G ) , E ( G ) are the vertex set and the edge set respectively and a G asssociates with each edge an ordered pair of vertices not necessarily distinct
a Helly circle graph if G is a circle graph and there exists a model of G by chords such that every three pairwise intersecting chords intersect at the same point