Smith's theorem and a characterization of the 6-cube as distance-transitive graph

Alfuraidan, M.R.; Hall, J.I.

Geodesic

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Smith's theorem and a characterization of the 6-cube as distance-transitive graph

Alfuraidan, M.R. ; Hall, J.I.

Journal of Algebraic Combinatorics, Tome 24 (2006) no. 2, pp. 195-207.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Résumé

Summary: A generic distance-regular graph is primitive of diameter at least two and valency at least three. We give a version of Derek Smith's famous theorem for reducing the classification of distance-regular graphs to that of primitive graphs. There are twelve cases-the generic case, four canonical imprimitive cases that reduce to the generic case, and seven exceptional cases. All distance-transitive graphs were previously known in six of the seven exceptional cases. We prove that the 6-cube is the only distance-transitive graph coming under the remaining exceptional case.

Keywords: keywords imprimitive distance-transitive graph, imprimitive distance-regular graph

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     title = {Smith's theorem and a characterization of the 6-cube as distance-transitive graph},
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Alfuraidan, M.R.; Hall, J.I. Smith's theorem and a characterization of the 6-cube as distance-transitive graph. Journal of Algebraic Combinatorics, Tome 24 (2006) no. 2, pp. 195-207. http://geodesic.mathdoc.fr/item/JAC_2006__24_2_a1/