Abstract
We consider the problem of construction of graphs with given degree $k$
and girth 5 and as few vertices as possible. We give a construction of a family
of girth 5 graphs based on relative difference sets. This family contains the
smallest known graph of degree 8 and girth 5 which was constructed by Royle,
four of the known cages including the Hoffman-Singleton graph, some graphs
constructed by Exoo and some new smallest known graphs.
| Original language | English |
|---|---|
| Journal | Discrete Mathematics |
| Volume | 293 |
| Issue number | 1-3 |
| Pages (from-to) | 177-184 |
| ISSN | 0012-365X |
| Publication status | Published - 2005 |
Keywords
- Cayley graph