On certain regular graphs of girth 5 - M. O'keefe; P. K. Wong (International Journal of Mathematics and Mathematical Sciences)
Let f(v,5) be the number of vertices of a (v,5)-cage (v≥3). We give an upper bound for f(v,5) which is considerably better than the previously known upper bounds. In particular, when v=7, it coincides with the well-known Hoffman- Singleton graph.