In this paper all graphs will be ordinary graphs, i.e. finite, undirected, and without loops or multiple edges. For points x and y of a graph G, we shall indicate that x is adjacent to y by writing x ⊥ y, and if x is not adjacent to y we shall write xy. We shall denote the degree of a point x by δ(x) and the minimal degree of G by δ(G).

By the line graph of a graph G we shall mean the graph L(G) whose points are the edges of G, with two points of L(G) adjacent whenever they are adjacent in G. A graph G is said to be a line graph if there exists a graph H such that G = L(H).