Families of small regular graphs of girth 5

In this paper we obtain (q+3−u)(q+3−u)-regular graphs of girth 5, for 1≤u≤q−11≤u≤q−1 with fewer vertices than previously known ones, for each prime q≥13q≥13, performing operations of reductions and amalgams on the Levi graph BqBq of an elliptic semiplane of type CC. We also obtain a 13-regular graph of girth 5 on 236 vertices from B11B11 using the same technique.