The Desargues graph is one of three cubic graphs on 20 nodes with smallest possible graph crossing
number of 6 (the others being two unnamed graphs denoted CNG 6B and CNG 6C by
Pegg and Exoo 2009), making it a smallest
cubic crossing number graph (Pegg and Exoo 2009, Clancy et al. 2019).
The Desargues is an integral graph with graph spectrum .
It is cospectral with another nonisomorphic
graph (Haemers and Spence 1995, van Dam and Haemers 2003).
It is also a unit-distance graph (Gerbracht
2008) and is 3-unitransitive (Harary 1994, p. 175).
The Desargues graph is the first of four graphs depicted on the cover of Harary (1994).
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