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  • Automorphism groups of Cayley graphs generated by block transpositions and regular Cayley maps
    Korchmaros, Annachiara ; Kovács, István, 1969-
    This paper deals with the Cayley graph ▫$\mathrm{Cay}(\mathrm{Sym}_n,T_n)$▫, where the generating set consists of all block transpositions. A motivation for the study of these particular Cayley ... graphs comes from current research in Bioinformatics. As the main result, we prove that ▫$\text{Aut}(\mathrm{Cay}(\mathrm{Sym}_n,T_n))$▫ is the product of the left translation group by a dihedral group ▫$\mathsf{D}_{n+1}$▫ of order ▫$2(n+1)$▫. The proof uses several properties of the subgraph ▫$\Gamma$▫ of ▫$\mathrm{Cay}(\mathrm{Sym}_n,T_n)$▫ induced by the set ▫$T_n$▫. In particular, ▫$\Gamma$▫ is a ▫$2(n-2)$▫-regular graph whose automorphism group is ▫$\mathsf{D}_{n+1}$▫, ▫$\Gamma$▫ has as many as ▫$n+1$▫ maximal cliques of size ▫$2$▫, and its subgraph ▫$\Gamma(V)$▫ whose vertices are those in these cliques is a ▫$3$▫-regular, Hamiltonian, and vertex-transitive graph. A relation of the unique cyclic subgroup of ▫$\mathsf{D}_{n+1}$▫ of order ▫$n+1$▫ with regular Cayley maps on ▫$\mathrm{Sym}_n$▫ is also discussed. It is shown that the product of the left translation group by the latter group can be obtained as the automorphism group of a non-▫$t$▫-balanced regular Cayley map on ▫$\mathrm{Sym}_n$▫.
    Vir: Discrete mathematics. - ISSN 0012-365X (Vol. 340, iss. 1, 2017, str. 3125-3139)
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2017
    Jezik - angleški
    COBISS.SI-ID - 1538911684

    Povezava(-e):

    http://dx.doi.org/10.1016/j.disc.2016.06.014

vir: Discrete mathematics. - ISSN 0012-365X (Vol. 340, iss. 1, 2017, str. 3125-3139)

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