English

Families of small regular graphs of girth 7

Combinatorics 2012-11-13 v1

Abstract

The first known families of cages arised from the incidence graphs of generalized polygons of order qq, qq a prime power. In particular, (q+1,6)(q+1,6)--cages have been obtained from the projective planes of order qq. Morever, infinite families of small regular graphs of girth 5 have been constructed performing algebraic operations on Fq\mathbb{F}_q. In this paper, we introduce some combinatorial operations to construct new infinite families of small regular graphs of girth 7 from the (q+1,8)(q+1,8)--cages arising from the generalized quadrangles of order qq, qq a prime power.

Keywords

Cite

@article{arxiv.1211.2672,
  title  = {Families of small regular graphs of girth 7},
  author = {M. Abreu and G. Araujo-Pardo and C. Balbuena and D. Labbate and J. Salas},
  journal= {arXiv preprint arXiv:1211.2672},
  year   = {2012}
}