line graph

noun3

1. •
   A graph in which a series of connected straight lines connect points, each of which represents the value of a particular variable as a function of another variable.
2. •
   A graph L(G) which is derived from a given non-oriented graph G such that the vertices of L(G) represent edges of G and so that a clique in L(G) represents a common end-vertex shared by a set of represented edges. (A star subgraph in G transforms into a clique in L(G).)
3. •
   A graph which is the line graph (in the above sense) of some other graph.

   • Suppose that a graph G has vertices A, B, C, and D such that A is adjacent to each of B, C, and D, but {B, C, D} is an independent set. Then G cannot be a line graph.