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Pappus graph

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Pappus graph
The Pappus graph, a Levi graph with 18 vertices formed from the Pappus configuration.
Named afterPappus of Alexandria
Vertices18
Edges27
PropertiesDistance-regular
Cubic
Table of graphs and parameters

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 Cubic symmetric graphs (The Foster Census). It has crossing number 5, and is the smallest cubic graph with that crossing number (sequence A110507 in the OEIS).

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

References

  • Kagno, I. N. (1947). "Desargues' and Pappus' graphs and their groups". American Journal of Mathematics. 69 (4): 859–863.
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