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https://doi.org/10.1007/978-3-211-71585-7s, and finite locally primitive graphs. The nature of the group theoretic techniques used range from elementary ones to some involving the finite simple group classification. In particular the theorem of O’Nan and Scott for finite primitive permutation groups, and a generalisation of it for finite quasiprimitive permutation groups is discussed.

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Finite transitive permutation groups and finite vertex-transitive graphs,s, and finite locally primitive graphs. The nature of the group theoretic techniques used range from elementary ones to some involving the finite simple group classification. In particular the theorem of O’Nan and Scott for finite primitive permutation groups, and a generalisation of it for finite quasiprimitive permutation groups is discussed.

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https://doi.org/10.1057/9780333985168oint work by P. Niemeyer and the author on fiber-equivalence, which is a refinement of end-equivalence. Section 6: the classification of locally finite, edge-transitive planar graphs by J.E. Graver and the author in terms of the number of ends, their Petrie walks, and the local behavior of their automorphism groups.

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https://doi.org/10.1007/978-981-16-9621-3 graph. Following this, we survey some basic material from permutation groups and model theory. Then we discuss various constructions and characterisations of infinite highly symmetric graphs, and connections with several topics in finite combinatorics, including random graphs, enumeration, and grap