a finite set, V(G) of objects, called "vertices", together with a set, E(G), of unordered pairs of distict vertices

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 k -tree if it is K k or is obtained from a k -tree by adding a new vertex adjacent to a k -clique

a minor of a graph H if H can be obtained from a subgraph of G by contracting edges

a set of vertex (nodes) v connected by edges (links) e

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