# What is a Line Graph in Math

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: 