2014•Mathematica SlovacaOpen access

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

Julie De Saedeleer, Dimitri Leemans, Mark Mixer, Tomaž Pisanski

Abstract

Abstract 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.

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Key concepts: Coset, Transitive relation, Mathematics, Combinatorics, Bipartite graph, Vertex (graph theory), Transitive reduction, Symmetric graph