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In mathematics, the Perkel graph, named after Manley Perkel, is a 6-regular graph with 57 vertices and 171 edges. It is the unique distance-regular graph with intersection array (6, 5, 2; 1, 1, 3).〔Coolsaet, K. and Degraer, J. "A Computer Assisted Proof of the Uniqueness of the Perkel Graph." Designs, Codes and Crypt. 34, 155–171, 2005.〕 The Perkel graph is also distance-transitive. It is also the skeleton of an abstract regular polytope, the 57-cell. == References== * Brouwer, A. E. ''Perkel Graph.'' (). * Brouwer, A. E.; Cohen, A. M.; and Neumaier, A. ''The Perkel Graph for L(2,19).'' 13.3 in Distance Regular Graphs. New York: Springer-Verlag, pp. 401–403, 1989. * Perkel, M. ''Bounding the Valency of Polygonal Graphs with Odd Girth.'' Canad. J. Math. 31, 1307-1321, 1979. * Perkel, M. ''Characterization of in Terms of Its Geometry.''Geom. Dedicata 9, 291-298, 1980. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Perkel graph」の詳細全文を読む スポンサード リンク
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