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Core-free, rank two coset geometries from edge-transitive bipartite graphs

par De Saedeleer, Julie ;Leemans, Dimitri ;Mixer, Mark ;Pisanski, Tomaž
Référence Mathematica slovaca, 64, 4, page (991-1006)
Publication Publié, 2014-08

Article révisé par les pairs

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Résumé :

It is known that the Levi graph of any rank two coset geometry is an edge-transitive graph, and thus coset geometries can be used to construct many edge transitive graphs. In this paper, we consider the reverse direction. Starting from edge-transitive graphs, we construct all associated core-free, rank two coset geometries. In particular, we focus on 3-valent and 4-valent graphs, and are able to construct coset geometries arising from these graphs. We summarize many properties of these coset geometries in a sequence of tables; in the 4-valent case we restrict to graphs that have relatively small vertex-stabilizers.