ترغب بنشر مسار تعليمي؟ اضغط هنا

Infinite arc-transitive and highly-arc-transitive digraphs

76   0   0.0 ( 0 )
 نشر من قبل R\\\"ognvaldur G. M\\\"oller
 تاريخ النشر 2018
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

A detailed description of the structure of two-ended arc-transitive digraphs is given. It is also shown that several sets of conditions, involving such concepts as Property Z, local quasi-primitivity and prime out-valency, imply that an arc-transitive digraph must be highly-arc-transitive. These are then applied to give a complete classification of two-ended highly-arc-transitive digraphs with prime in- and out-valencies.



قيم البحث

اقرأ أيضاً

A general method for constructing sharply $k$-arc-transitive digraphs, i.e. digraphs that are $k$-arc-transitive but not $(k+1)$-arc-transitive, is presented. Using our method it is possible to construct both finite and infinite examples. The infinit e examples can have one, two or infinitely many ends. Among the one-ended examples there are also digraphs that have polynomial growth.
Given integers $k$ and $m$, we construct a $G$-arc-transitive graph of valency $k$ and an $L$-arc-transitive oriented digraph of out-valency $k$ such that $G$ and $L$ both admit blocks of imprimitivity of size $m$.
This paper begins the classification of all edge-primitive 3-arc-transitive graphs by classifying all such graphs where the automorphism group is an almost simple group with socle an alternating or sporadic group, and all such graphs where the automo rphism group is an almost simple classical group with a vertex-stabiliser acting faithfully on the set of neighbours.
We introduce the notion of a symmetric basis of a vector space equipped with a quadratic form, and provide a sufficient and necessary condition for the existence to such a basis. Symmetric bases are then used to study Cayley graphs of certain extrasp ecial 2-groups of order 2^{2r+1} (rgeq 1), which are further shown to be normal Cayley graphs and 2-arc-transitive covers of 2r-dimensional hypercubes.
80 - Zaiping Lu 2018
A graph is edge-primitive if its automorphism group acts primitively on the edge set. In this short paper, we prove that a finite 2-arc-transitive edge-primitive graph has almost simple automorphism group if it is neither a cycle nor a complete bipar tite graph. We also present two examples of such graphs, which are 3-arc-transitive and have faithful vertex-stabilizers.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا