Locally Symmetric Graphs of Girth 4 |
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| Authors: | Micha A Perles Horst Martini Yaakov S Kupitz |
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| Institution: | 1. INSTITUTE OF MATHEMATICS, THE HEBREW UNIVERSITY OF JERUSALEM, , JERUSALEM, ISRAEL;2. FAKULT?T FüR MATHEMATIK, , 09107 CHEMNITZ, GERMANY |
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| Abstract: | 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. |
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| Keywords: | automorphism group bipartite graph Heawood and co-Heawood graph Coxeter graph Fano plane girth of a graph (hyperbolic) honeycomb Klein map ‐regular graph locally symmetric graph matching 120-cell Petersen graph regular dodecahedron Riemann surface tessellation bathroom tiling MSC (2000) :05C12 05C30 51E30 94C15 |
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