Pappus graph

Pappus graph

infobox graph
name = Pappus graph


image_caption = The Pappus graph, a Levi graph with 18 vertices formed from the Pappus configuration.
namesake = Pappus of Alexandria
vertices = 18
edges = 27
chromatic_number =
chromatic_index =
properties = Distance-regular Cubic

In the mathematical field of graph theory, the Pappus graph is a 3-regular graph with 18 vertices and 27 edges, formed as the Levi graph of the Pappus configuration. It is a distance-regular graph, one of only 14 such cubic graphs according to [http://www.csse.uwa.edu.au/~gordon/remote/foster/#drgs Cubic symmetric graphs (The Foster Census)] . It has crossing number 5, and is the smallest cubic graph with that crossing number OEIS|id=A110507.

The name "Pappus graph" has also been used to refer to a related nine-vertex graph (Kagno 1947).

References

* citation
last = Kagno | first = I. N.
title = Desargues' and Pappus' graphs and their groups
journal = American Journal of Mathematics
year = 1947
volume = 69
issue = 4
pages = 859–863
doi = 10.2307/2371806

External links

*


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