Foster graph

Foster graph

infobox graph
name = Foster graph


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In graph theory the Foster graph is a graph on 90 vertices and 135 arcs. It is the unique distance-transitive graph with intersection array {3,2,2,2,2,1,1,1;1,1,1,1,2,2,2,3}. It can be constructed as the incidence graph of the partial linear space which is the unique triple cover with no 8-gons of the generalized quadrangle "GQ"(2,2).

References

*citation
last1 = Biggs | first1 = N. L. | last2 = Boshier | first2 = A. G. | last3 = Shawe-Taylor | first3 = J.
title = Cubic distance-regular graphs
journal = Journal of the London Mathematical Society
volume = 33 | issue = 3 | year = 1986 | pages = 385–394
doi = 10.1112/jlms/s2-33.3.385
id = MathSciNet | id = 0850954.

*citation
last1 = Van Dam | first1 = Edwin R. | last2 = Haemers | first2 = Willem H.
title = Spectral characterizations of some distance-regular graphs
journal = Journal of Algebraic Combinatorics
volume = 15 | issue = 2 | year = 2002 | pages = 189–202
id = MathSciNet | id = 1887234
doi = 10.1023/A:1013847004932.

*citation
last = Van Maldeghem | first = Hendrik
title = Ten exceptional geometries from trivalent distance regular graphs
journal = Annals of Combinatorics
volume = 6 | issue = 2 | year = 2002 | pages = 209–228
id = MathSciNet | id = 1955521
doi = 10.1007/PL00012587.

External links

* [http://www.win.tue.nl/~aeb/graphs/cubic_drg.html Cubic distance-regular graphs] , A. Brouwer.
*mathworld|title=Foster Graph|urlname=FosterGraph


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