Families of Small Regular Graphs of Girth 5

Abstract

In this paper we obtain $(q+3)$--regular graphs of girth 5 with fewer vertices than previously known ones for $q=13,17,19$ and for any prime $q\ge 23$ performing operations of reductions and amalgams on the Levi graph $B_q$ of an elliptic semiplane of type $\mathcal{C}$. We also obtain a 13-regular graph of girth 5 on 236 vertices from $B_{11}$ using the same technique.