Analysing finite locally $s$-arc transitive graphs
نویسندگان
چکیده
منابع مشابه
ANALYSING FINITE LOCALLY s-ARC TRANSITIVE GRAPHS
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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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...
متن کاملWeakly 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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Let Γ be a finite locally (G, s)-arc transitive graph with s ≥ 2 such that G is intransitive on vertices. Then Γ is bipartite and the two parts of the bipartition are G-orbits. In previous work the authors showed that if G has a nontrivial normal subgroup intransitive on both of the vertex orbits of G, then Γ is a cover of a smaller locally s-arc transitive graph. Thus the “basic” graphs to stu...
متن کاملCountable locally 2-arc-transitive bipartite graphs
We present an order-theoretic approach to the study of countably infinite locally 2-arc-transitive bipartite graphs. Our approach is motivated by techniques developed by Warren and others during the study of cycle-free partial orders. We give several new families of previously unknown countably infinite locally-2-arc-transitive graphs, each family containing continuum many members. These exampl...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2003
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-03-03361-0