An explicit formula for obtaining $(q+1,8)$-cages and others small regular graphs of girth 8

Details An explicit formula for obtaining $(q+1,8)$-cages and others small regular graphs of girth 8 An explicit formula for obtaining $(q+1,8)$-cages and others small regular graphs of girth 8

2011-11-14

arxiv.org/abs/1111.3279v1

Mathematics

Combinatorics

Scientific paper

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.

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