Line graph

Name

The construction outlined here goes by the name of the line graph. Alternate names are the theta-obrazom, the covering graph, the derivative, the edge-to-vertex dual, the conjugate, and the representative graph, as well as the edge graph, the interchange graph, the adjoint graph, and the derived graph.

Definition

Suppose $G$ is an undirected graph. The line graph of $G$, denoted $L(G)$, is defined as follows:

1. The vertex set of $L(G)$ is defined as the edge set of $G$.
2. The edges of $L(G)$ are defined as follows: two vertices of $L(G)$ are adjacent if and only if, when viewed as edges of $G$, they share a common vertex.