s-Arc-transitive graphs and normal subgroups
نویسندگان
چکیده
منابع مشابه
Weakly s-arc transitive graphs
Weakly s-arc transitive graphs are introduced and determined. A graph is said to be weakly s-arc transitive if its endomorphism monoid acts transitively on the set of s-arcs. The main results are: (1) A nonbipartite graph is weakly s-arc transitive if and only if it is s-arc transitive. (2) A tree with diameter d is weakly s-arc transitive for all 0 s d. (3) A bipartite graph with girth g = 2s ...
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We present a new approach to analysing finite graphs which admit a vertex intransitive group of automorphisms G and are either locally (G, s)– arc transitive for s ≥ 2 or G–locally primitive. Such graphs are bipartite with the two parts of the bipartition being the orbits of G. Given a normal subgroup N which is intransitive on both parts of the bipartition, we show that taking quotients with r...
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For two normal edge-transitive Cayley graphs on groups H and K which have no common direct factor and $gcd(|H/H^prime|,|Z(K)|)=1=gcd(|K/K^prime|,|Z(H)|)$, we consider four standard products of them and it is proved that only tensor product of factors can be normal edge-transitive.
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An s-arc in a graph is a vertex sequence (α0, α1, . . . , αs) such that {αi−1, αi} ∈ EΓ for 1 6 i 6 s and αi−1 6= αi+1 for 1 6 i 6 s− 1. This paper gives a characterization of a class of s-transitive graphs; that is, graphs for which the automorphism group is transitive on s-arcs but not on (s+ 1)-arcs. It is proved that if Γ is a finite connected s-transitive graph (where s > 2) of order a p-p...
متن کاملLocally s - arc transitive graphs with two different quasiprimitive actions ?
Previous work of the authors has shown that an important class of locally (G, 2)arc transitive graphs are those for which G acts faithfully and quasiprimitively on each of its two orbits on vertices. In this paper we give a complete classification in the case where the two quasiprimitive actions of G are of different types. The graphs obtained have amalgams previously unknown to the authors and...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2015
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2014.08.032