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 graph

Facts about Line graph

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.

Check Also: 10 Facts about Leonardo Fibonacci

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

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

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.

See Also: 10 Facts about Large Numbers

Facts about Line Graphs 9: the various generalizations of line graphs

The line graphs have various generalizations, which may include the line graphs of weighted graphs, the line graphs of hypergraphs, line graphs of multigraphs, and line graphs of line graphs.

Facts about Line Graphs 10: how to study line graphs

If you are interested to study line graphs, the books, papers and publications about it are available. You can read the works of Whitney or even Krausz.

What do you think on facts about line graphs?