Families of small regular graphs of girth 5

In this paper we obtain ( q + 3 − u ) -regular graphs of girth 5, for 1 ≤ u ≤ q − 1 with fewer vertices than previously known ones, for each prime q ≥ 13 , performing operations of reductions and amalgams on the Levi graph B q of an elliptic semiplane of type C . We also obtain a 13-regular graph of girth 5 on 236 vertices from B 11 using the same technique.