Finite $s$-arc transitive Cayley graphs and flag-transitive projective planes
نویسندگان
چکیده
منابع مشابه
FINITE s-ARC TRANSITIVE CAYLEY GRAPHS AND FLAG-TRANSITIVE PROJECTIVE PLANES
In this paper, a characterisation is given of finite s-arc transitive Cayley graphs with s ≥ 2. In particular, it is shown that, for any given integer k with k ≥ 3 and k 6= 7, there exists a finite set (maybe empty) of s-transitive Cayley graphs with s ∈ {3, 4, 5, 7} such that all s-transitive Cayley graphs of valency k are their normal covers. This indicates that s-arc transitive Cayley graphs...
متن کاملWeakly Flag-transitive Configurations and Half-arc-transitive Graphs
A con guration is weakly ag transitive if its group of automor phisms acts intransitively on ags but the group of all automorphisms and anti automorphisms acts transitively on ags It is shown that weakly ag transitive con gurations are in one to one correspondence with bipartite arc transitive graphs of girth not less than Sev eral in nite families of weakly ag transitive con gurations are gi...
متن کاملWeakly Flag-transitive Configurations and Half-arc-transitive Graphs
A connguration is weakly ag-transitive if its group of automor-phisms acts intransitively on ags but the group of all automorphisms and anti-automorphisms acts transitively on ags. It is shown that weakly ag-transitive conngurations are in one-to-one correspondence with bipartite 1 2-arc-transitive graphs of girth not less than 6. Several innnite families of weakly ag-transitive conngurations a...
متن کاملANALYSING 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...
متن کامل5-Arc transitive cubic Cayley graphs on finite simple groups
In this paper, we determine all connected 5-arc transitive cubic Cayley graphs on the alternating group A47; there are only two such graphs (up to isomorphism). By earlier work of the authors, these are the only two nonnormal connected cubic arc-transitive Cayley graphs for finite nonbelian simple groups, and so this paper completes the classification of such non-normal Cayley graphs.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2004
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-04-07549-5