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Home > Vol 22, No 4 (2005)

Sanming Zhou

The University of Melbourne Department of Mathematics and Statistics Parkville VIC 3010 Australia Parkville VIC 3010 Australia

Let \? be a G-symmetric graph admitting a nontrivial G-invariant partition B {\cal B} . Let \? _B _{\cal B} be the quotient graph of \? with respect to B {\cal B} . For each block B ϵ  B {\cal B} , the setwise stabiliser G _B of B in G induces natural actions on B and on the neighbourhood \? _B _{\cal B} ( B) of B in \? _B _{\cal B} . Let G _{( B)} and G _{[ B]} be respectively the kernels of these actions. In this paper we study certain “local actions" induced by G _{( B)} and G _{[ B]}, such as the action of G _{[ B]} on B and the action of G _{( B)} on \? _B _{\cal B} ( B), and their influence on the structure of \?.

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