Analysing Finite Locally s-arc Transitive Graphs

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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 greater than or equal to 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 respect to the orbits of N preserves both local primitivity and local s-arc transitivity and leads us to study graphs where G acts faithfully on both orbits and quasiprimitively on at least one. We determine the possible quasiprimitive types for G in these two cases and give new constructions of examples for each possible type. The analysis raises several open problems which are discussed in the final section.
Original languageEnglish
Pages (from-to)291-317
JournalTransactions of the American Mathematical Society
Issue number1
Publication statusPublished - 2004


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