Given a graph G, its line graph L(G) is a graph such that
• each vertex of L(G) represents an edge of G; and
• two vertices of L(G) are adjacent if and only if their corresponding edges share a common … 展开

Clique partition
For an arbitrary graph G, and an arbitrary vertex v in G, the set of edges incident to v corresponds to a clique in the line graph L(G). The cliques formed in this way partition the edges of L(G). Each vertex of L(G) belongs to exactly … 展开

Medial graphs and convex polyhedra
When a planar graph G has maximum vertex degree three, its line graph is planar, and every planar … 展开

The following figures show a graph (left, with blue vertices) and its line graph (right, with green vertices). Each vertex of the line graph is shown labeled with the pair of endpoints of the … 展开

Translated properties of the underlying graph
Properties of a graph G that depend only on adjacency between edges may be translated into equivalent … 展开

van Rooij & Wilf (1965) consider the sequence of graphs
They show that, when G is … 展开

1. ^ Hemminger & Beineke (1978), p. 273.
2. ^ Harary (1972), p. 71.
3. ^ Whitney (1932); Krausz (1943); Harary (1972), Theorem 8.3, p. 72. Harary gives a simplified proof of this theorem by Jung (1966). 展开