# 10 Facts about Line Graphs

Post On: January 31, 2017
By: Agustina

If you are interested to study mathematics, Facts about Line Graphs will expand your insights. It is a branch of graph theory. Harary & Norman had a paper published in 1960, which coined the term line graph. However, the construction of line graph actually had been traced back in 1932 and 1943 by Whitney and Krausz respectively. Here are other interesting facts about line graph to notice:

## Facts about Line Graphs 1: the terms of line graphs

Line graph has various terms. You may call it the adjoint graph, edge-to-vertex dual, covering graph, interchange graph, edge graph, representative graph, derivative the derived graph, or the conjugate. ### Facts about Line Graphs 2: the function of line graph

The line graph was used to recover the structure of a connected graph G according to Hassler Whitney (1932). He proved it.

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## Facts about Line Graphs 3: the characteristics of line graph

Can you mention some characteristics of line graph? The perfect feature is spotted on the line graph of bipartite graph. The claw-free one is seen in all line graphs.

### Facts about Line Graphs 4: how to recognize the line graph

Have you realized the way to recognize the line graph?  All of them are recognizable in linear time. Line graph Facts

## Facts about Line Graphs 5: another characteristic

The nine forbidden subgraphs are considered as the characteristics of the line graphs.

### Facts about Line Graphs 6: the properties

The underlying graphs from the vertices to the edges can be used to translate the properties of line graphs. Line graph Pic

## Facts about Line Graphs 7:  the theorem

You may apply the theorem about line graph developed by Whitney if you are interested to use the other direction for translating its properties.

### Facts about Line Graphs 8: the studies of line graph

Line graph is one of the most important fields in mathematics. There is no need to wonder that many scientists have studied and researched the different kinds of generalizations of line graphs.