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Weakly distance-regular digraphs with \(P\)-polynomial property

曾青 Qing Zeng

Beijing Normal University

Time: 16:00-17:00 (GMT+8), Wednesday June 5th, 2024
Location: Zoom

Abstract: Distance-regular graphs are an important class of graphs, which are equivalent to symmetric \(P\)-polynomial association schemes and have close connections to graph theory, finite geometry, coding theory, and design theory. As a directed version of distance-regular graphs, weakly distance-regular digraphs were proposed by Wang and Suzuki in 2003, which correspond to non-symmetric association schemes. In this thesis, we initiate studying weakly distance-regular digraphs with \(P\)-polynomial property, characterize weakly distance-regular digraphs whose attached schemes are \(P\)-polynomial, and classify all commutative weakly distance-regular digraphs whose underlying graphs are Hamming graphs, folded $n$-cubes, Doob graphs, and Johnson graphs, respectively.

Host: 尹富纲 Fu-Gang Yin