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 Km,n(2≤m<n). There are, up to isomorphism, exactly four such k-regular graphs for every 4≤k<∞, one for k=2, two for k=3, and exactly three for every infinite cardinal k. In the last paragraph, we consider locally symmetric graphs of girth >4.
| Original language | English |
|---|---|
| Pages (from-to) | 44-65 |
| Number of pages | 22 |
| Journal | Journal of Graph Theory |
| Volume | 73 |
| Issue number | 1 |
| DOIs | |
| State | Published - May 2013 |
Keywords
- (hyperbolic) honeycomb
- 120-cell
- automorphism group
- bathroom tiling
- bipartite graph
- Coxeter graph
- Fano plane
- girth of a graph
- Heawood and co-Heawood graph
- Klein map { 7, 3 } 8; k -regular graph
- locally symmetric graph
- matching
- MSC (2000):05C12, 05C30, 51E30, 94C15
- Petersen graph
- regular dodecahedron
- Riemann surface
- tessellation