Geodesic
On the Godsil--Higman necessary condition for equitable partitions of association schemes
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 10 (2013), pp. 699-704.

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In his monograph 'Association schemes', C. Godsil derived a necessary condition for equitable partitions of association schemes and noticed that it could be used to show that certain equitable partitions do not exist. In this short note, we show that, in fact, this condition is not stronger than the well-known Lloyd theorem.
Mots-clés : association scheme, equitable partition. 
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A. L. Gavrilyuk; I. Yu. Mogilnykh. On the Godsil--Higman necessary condition for equitable partitions of association schemes. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 10 (2013), pp. 699-704. http://geodesic.mathdoc.fr/item/SEMR_2013_10_a40/

[1] E. Bannai, T. Ito, Algebraic combinatorics, v. I, Benjamin/Cummings Publishing Co. Inc., Menlo Park, CA, 1984 | MR | Zbl

[2] A. E. Brouwer, A. M. Cohen, A. Neumaier, Distance regular graphs, Springer-Verl., Berlin, 1989 | MR | Zbl

[3] P. J. Cameron, Permutation groups, London Math. Soc. Student Texts, 45, Cambridge Univ. Press, Cambridge, 1999 | MR | Zbl

[4] P. Delsarte, “An algebraic approach to the association schemes of coding theory”, Philips Res. Rep. Suppl., 10 (1973), 1–97 | MR

[5] C. Godsil, R. Gordon, Algebraic graph theory, Springer Science+Business Media, LLC, 2004 | MR

[6] C. Godsil, Association schemes, University of Waterloo, 2010

[7] C. Godsil, “Compact Graphs and Equitable Partitions”, Linear Algebra And Its Applications, 255:1–3 (1997), 259–266 | MR | Zbl

[8] A. A. Makhnev, “On automorphisms of distance-regular graphs”, J. Math. Sci. (New York), 166:6 (2010), 733–742 | MR

[9] Martin W. J., Completely regular subsets, Ph. D. thesis, University of Waterloo, 1992 pp. | MR

[10] F. Vanhove, Incidence geometry from an algebraic graph theory point of view, Ph. D. Thesis, University of Ghent, 2011