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  • Cayley numbers with arbitrarily many distinct prime factors
    Dobson, Edward Tauscher, 1965- ; Spiga, Pablo
    A positive integer ▫$n$▫ is a Cayley number if every vertex-transitive graph of order ▫$n$▫ is a Cayley graph. In 1983, D. Marušič [Ars Comb. 16-B, 297--302 (1983)] posed the problem of determining ... the Cayley numbers. In this paper we give an infinite set ▫$S$▫ of primes such that every finite product of distinct elements from ▫$S$▫ is a Cayley number. This answers an outstanding question of B. D. McKay and C. E. Praeger [J. Graph Theory 22, No. 4, 321--334 (1996)], which they "believe to be the key unresolved question" on Cayley numbers. We also show that, for every finite product ▫$n$▫ of distinct elements from ▫$S$▫, every transitive group of degree ▫$n$▫ contains a semiregular element.
    Source: Journal of combinatorial theory. Series B. - ISSN 0095-8956 (Vol. 122, Jan. 2017, str. 301-310)
    Type of material - article, component part ; adult, serious
    Publish date - 2017
    Language - english
    COBISS.SI-ID - 1538528196

    Link(s):

    https://doi.org/10.1016/j.jctb.2016.06.005
    DOI

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