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Locally Symmetric Graphs of Girth 4


  • Contract grant sponsor: Deutsche Forschungsgemeinschaft and Landau Center (to Y.K.).


We classify the family of connected, locally symmetric graphs of girth 4 (finite and infinite). They are all regular, with the exception of the complete bipartite graph math formula. There are, up to isomorphism, exactly four such k-regular graphs for every math formula, one for math formula, two for math formula, and exactly three for every infinite cardinal k. In the last paragraph, we consider locally symmetric graphs of girth >4.