Abstract
Let Г be a G-symmetric graph admitting a nontrivial G-invariant partition \({\cal B}\). Let Г\(_{\cal B}\) be the quotient graph of Г with respect to \({\cal B}\). For each block B ∊ \({\cal B}\), the setwise stabiliser G B of B in G induces natural actions on B and on the neighbourhood Г\(_{\cal B}\)(B) of B in Г\(_{\cal B}\). 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 Г\(_{\cal B}\)(B), and their influence on the structure of Г.
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Supported by a Discovery Project Grant (DP0558677) from the Australian Research Council and a Melbourne Early Career Researcher Grant from The University of Melbourne.
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Zhou, S. A Local Analysis of Imprimitive Symmetric Graphs. J Algebr Comb 22, 435–449 (2005). https://doi.org/10.1007/s10801-005-4627-z
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DOI: https://doi.org/10.1007/s10801-005-4627-z