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  • A note on non-diagonalizable vertex-primitive digraphs [Elektronski vir]
    Razafimahatratra, Andriaherimanana Sarobidy
    In the 1980s, P. J. Cameron asked whether the adjacency matrix of any arc-transitive digraph is diagonalizable. Babai gave a negative answer to this question and posed a problem regarding the ... existence of vertexprimitive digraphs whose adjacency matrices are non-diagonalizable. Recently, Li, Xia, Zhou and Zhu constructed an infinite family of such digraphs and gave some finite examples which are not Cayley digraphs. Among these finite examples was a digraph arising from the action of PSL2(17) on 2-subsets of the projective line PG1(17). In this note, we show that the smallest vertex-primitive digraphs whose adjacency matrices are non-diagonalizable arise from the action of PSL2(17) on 2- subsets of PG1(17). We also show that the automorphism group of a non-diagonalizable vertex-primitive digraph is of almost simple type, diagonal type, or product type.
    Vir: The Australasian journal of combinatorics [Elektronski vir]. - ISSN 2202-3518 (Vol. 89, iss. 2, 2024, str. 305-322)
    Vrsta gradiva - e-članek ; neleposlovje za odrasle
    Leto - 2024
    Jezik - angleški
    COBISS.SI-ID - 199604995

    Povezava(-e):

    https://ajc.maths.uq.edu.au/pdf/89/ajc_v89_p305.pdf

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