Locally Symmetric Graphs of Girth 4
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 . There are, up to isomorphism, exactly four such k-regular graphs for every , one for , two for , and exactly three for every infinite cardinal k. In the last paragraph, we consider locally symmetric graphs of girth >4.
locally symmetric graph bipartite graph automorphism group heawood and co-heawood graph coxeter graph fano plane girth of a graph (hyperbolic) honeycomb klein map -regular graph matching 120-cell petersen graph regular dodecahedron riemann surface tessellation bathroom tiling msc (2000) :05c12 05c30 51e30 94c15