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  • Arc-transitive cubic abelian bi-Cayley graphs and BCI-graphs
    Koike Quintanar, Sergio Hiroki ; Kovács, István, 1969-
    A finite simple graph is called a bi-Cayley graph over a group ▫$H$▫ if it has a semiregular automorphism group, isomorphic to ▫$H$▫, which has two orbits on the vertex set. Cubic vertex-transitive ... bi-Cayley graphs over abelian groups have been classified recently by Feng and Zhou (Europ. J. Combin. 36 (2014), 679--693). In this paper we consider the latter class of graphs and select those in the class which are also arc-transitive. Furthermore, such a graph is called ▫$0$▫-type when it is bipartite, and the bipartition classes are equal to the two orbits of the respective semiregular automorphism group. A ▫$0$▫-type graph can be represented as the graph ▫$\mathrm{BiCay}(H,S),$▫ where ▫$S$▫ is a subset of ▫$H$▫, the vertex set of which consists of two copies of ▫$H$▫ say ▫$H_0$▫ and ▫$H_1$▫, and the edge set is ▫$\{\{h_0,g_1\} : h,g \in H, g h^{-1} \in S\}$▫. A bi-Cayley graph ▫$\mathrm{BiCay}(H,S)$▫ is called a BCI-graph if for any bi-Cayley graph ▫$\mathrm{BiCay}(H,T)$▫, ▫$\mathrm{BiCay}(H,S) \cong \mathrm{BiCay}(H,T)$▫ implies that ▫$T = h S^\alpha$▫ for some ▫$h \in H$▫ and ▫$\alpha \in \mathrm{Aut}(H)$▫. It is also shown that every cubic connected arc-transitive v$0$v-type bi-Cayley graph over an abelian group is a BCI-graph.
    Vir: Filomat. - ISSN 0354-5180 (Vol. 30, iss. 2, 2016, str. 321-331)
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2016
    Jezik - angleški
    COBISS.SI-ID - 1538911940

    Povezava(-e):

    http://dx.doi.org/10.2298/FIL1602321K

vir: Filomat. - ISSN 0354-5180 (Vol. 30, iss. 2, 2016, str. 321-331)

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