A line graph of an undirected graph G is other graph L(G) that symbolizes the adjacencies among edges of G. The name line graph comes through a paper by Norman and Harary even though both Krausz (1943) and Whitney (1932) employed the construction before this.

Other terms utilized for the line graph contain the covering
graph, the theta-obrazom, the edge-to-vertex dual, the derivative, the
conjugate and the edge graph and the representative graph, the adjoint graph,
the interchange graph and the derived graph.

**Formal Definition**

Given a graph G, its line graph L(G) is actually a graph
such that

every vertex of L(G) symbolizes an edge of G; and

2 vertices of L(G) are adjacent if and only if their related
edges share a common endpoint in G.

That is, it is the intersection graph with the edges of G,
symbolizing each edge by the pair of its two endpoints.

**Straight
Line Graph**

Straight line graphs are unique graphs which are originally
developed as part of a graphic approach. They are intended for symbolizing
growth data in a way to facilitate analysis and prediction. Their principle
feature is that the development lines of the legs could be represented as
straight lines.

Suppose you possess y = 3x + 2. Because this has just x, as
opposed to x2 or |x|, this graphs as simply a plain straight line. The very
first thing you need to do is draw what is known as a T-chart. It looks like
this: