"The" Sylvester graph is a quintic graph on 36 nodes and 90 edges that is the unique distance-regular
graph with intersection array et al. 1989, §13.1.2; Brouwer
and Haemers 1993). It is a subgraph of the Hoffman-Singleton
graph obtainable by choosing any edge, then deleting the 14 vertices within distance
2 of that edge.
It has graph diameter 3, girth 5, graph radius 3, is Hamiltonian, and nonplanar.
It has chromatic number 4, edge
connectivity 5, vertex connectivity 5,
and edge chromatic number 5.
It is an integral graph and has graph spectrum
The Sylvester graph of a configuration is the set of ordinary
points and ordinary lines .
See also Distance-Regular Graph ,
Integral Graph ,
Ordinary
Line ,
Ordinary Point
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References Brouwer, A. E. "Sylvester Graph." http://www.win.tue.nl/~aeb/drg/graphs/Sylvester.html . Brouwer, A. E.; Cohen, A. M.; and Neumaier, A. §13.1.2 in Distance
Regular Graphs. Brouwer, A. E.
and Haemers, W. H. "The Gewirtz Graph: An Exercise in the Theory of Graph
Spectra." European J. Combin. 14 , 397-407, 1993. DistanceRegular.org.
"Sylvester Graph." http://www.distanceregular.org/graphs/sylvester.html . Guy,
R. K. "Monthly Unsolved Problems, 1969-1987." Amer. Math. Monthly 94 ,
961-970, 1987. Guy, R. K. "Unsolved Problems Come of Age."
Amer. Math. Monthly 96 , 903-909, 1989. Referenced on Wolfram|Alpha Sylvester Graph
Cite this as:
Weisstein, Eric W. "Sylvester Graph."
From MathWorld https://mathworld.wolfram.com/SylvesterGraph.html
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(Brouwer et al. 1989, §13.1.2; Brouwer
and Haemers 1993). It is a subgraph of the Hoffman-Singleton
graph obtainable by choosing any edge, then deleting the 14 vertices within distance
2 of that edge.
(Brouwer and Haemers 1993).
