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Local McLaughlin Graph

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The local McLaughlin graph is the slightly unfortunate name given to the graph on 162 vertices and 4536 edges obtained from the McLaughlin graph by vertex deletion of a single vertex and its neighbors. It is therefore a subconstituent of the McLaughlin graph.

The Local McLaughlin graph is implemented in the Wolfram Language as GraphData["LocalMcLaughlinGraph"].

It is a strongly regular graph with parameters (162,56,10,24). It is determined by spectrum and has graph spectrum (-16)^(21)2^(140)56^1 (van Dam and Haemers 2003). It has independence number 21 and 324 maximum independent vertex sets (Brouwer).

It is however not the local graph of the McLaughlin graph; in fact the local graph of the McLaughlin graph is the generalized quadrangle GQ(3,9).

See also

Local Graph, McLaughlin Graph

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References

Brouwer, A. E. "U_4(3) on 162 Points." https://aeb.win.tue.nl/graphs/U4_3a.html.Cameron, P. J.; Goethals, J. M.; and Seidel, J. J. "Strongly Regular Graph having Strongly Regular Subconstituents." J. Algebra 55, 257-280, 1978.Godsil, C. and Royle, G. Algebraic Graph Theory. New York: Springer-Verlag, 2001.House of Graphs. "Local Mc Laughlin Graph." https://houseofgraphs.org/graphs/1212.Soicher, L. H. "Three New Distance-Regular Graphs." Europ. J. Combin. 14, 501-505, 1993.van Dam, E. R. and Haemers, W. H. "Spectral Characterizations of Some Distance-Regular Graphs." J. Algebraic Combin. 15, 189-202, 2003.

Referenced on Wolfram|Alpha

Local McLaughlin Graph

Cite this as:

Weisstein, Eric W. "Local McLaughlin Graph." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/LocalMcLaughlinGraph.html

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