9 research outputs found
Dva-ločno-tranzitivni dvo-valentni digrafi določenih redov
The topic of this paper is digraphs of in-valence and out-valence 2 that admit a 2-arc-transitive group of automorphisms. We classify such digraphs that satisfy certain additional conditions on their order. In particular, a classification of those with order ▫▫ or ▫▫ where ▫▫ and ▫▫ is a prime can be deduced from the results of this paper.Tema tega članka so digrafi vhodne in izhodne valence 2, ki dopuščajo 2-ločno-tranzitivno grupo avtomorfizmov. Klasificiramo takšne digrafe, ki zadoščajo določenim dodatnim pogojem glede njihovega reda. Tako je npr. mogoče s pomočjo rezultatov tega članka klasificirati tiste, ki imajo red ▫▫ ali ▫▫, kjer je ▫▫ in je ▫▫ praštevilo
Recent trends and future directions in vertex-transitive graphs
A graph is said to be vertex-transitive if its automorphism group acts transitively on the vertex set. Some recent developments and possible future directions regarding two famous open problems, asking about existence of Hamilton paths and existence of semiregular automorphisms in vertex-transitive graphs, are discussed, together with some recent results on arc-transitive graphs and half-arc-transitive graphs, two special classes of vertex-transitive graphs that have received particular attention over the last decade
On tetravalent half-arc-transitive graphs of girth 5
A subgroup of the automorphism group of a graph \G is said to be {\em
half-arc-transitive} on \G if its action on \G is transitive on the vertex
set of \G and on the edge set of \G but not on the arc set of \G.
Tetravalent graphs of girths and admitting a half-arc-transitive group
of automorphisms have previously been characterized. In this paper we study the
examples of girth . We show that, with two exceptions, all such graphs only
have directed -cycles with respect to the corresponding induced orientation
of the edges. Moreover, we analyze the examples with directed -cycles, study
some of their graph theoretic properties and prove that the -cycles of such
graphs are always consistent cycles for the given half-arc-transitive group. We
also provide infinite families of examples, classify the tetravalent graphs of
girth admitting a half-arc-transitive group of automorphisms relative to
which they are tightly-attached and classify the tetravalent
half-arc-transitive weak metacirculants of girth
On the vertex-stabiliser in arc-transitive digraphs
AbstractWe discuss a possible approach to the study of finite arc-transitive digraphs and prove an upper bound on the order of a vertex-stabiliser in locally cyclic arc-transitive digraphs of prime out-valence
Bridging Semisymmetric And Half-Arc-Transitive Actions On Graphs
A generalization of some of the Folkman's constructions [13] of the so called semisymmetric graphs, that is regular graphs which are edge- but not vertex-transitive, was given in [22] together with a natural connection of graphs admittin