International Journal of Mathematics and Mathematical Sciences
Volume 7 (1984), Issue 4, Pages 785-791

On certain regular graphs of girth 5

M. O'keefe and P. K. Wong

Department of Mathematics, Seton Hall University, South Orange 07079, New Jersey, USA

Received 23 May 1984

Copyright © 1984 M. O'keefe and P. K. Wong. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Let f(v,5) be the number of vertices of a (v,5)-cage (v3). 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.