Let q be a prime power; (q+1,8)-cages have been constructed as incidence graphs of a non-degenerate quadric surface in projective 4-space P(4,q). The first contribution of this paper is a construction of these graphs in an alternative way by means of an explicit formula using graphical terminology. Furthermore by removing some specific perfect dominating sets from a (q+1,8)-cage we derive k-regular graphs of girth 8 for k=q−1 and k=q, having the smallest number of vertices known so far.
@article{arxiv.1111.3279,
title = {An explicit formula for obtaining $(q+1,8)$-cages and others small regular graphs of girth 8},
author = {M. Abreu and G. Araujo-Pardo and C. Balbuena and D. Labbate},
journal= {arXiv preprint arXiv:1111.3279},
year = {2011}
}