2011/06/28 by Julie De Saedeleer, Dimitri Leemans, De Saedeleer, Julie +5
Mathematics · #05B20 #05C62 #20B25 #51A10 #51E30 #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #math.AG #math.CO #math.GR #msc:05B20 #msc:05C62 #msc:20B25 #msc:51A10 #msc:51E30
paper · pdf · doi:10.48550/arxiv.1106.5704
arxiv created 2011/06/29 · arxiv updated 2011/06/30
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.