Families of small regular graphs of girth 7
Abstract
The first known families of cages arised from the incidence graphs of generalized polygons of order q, q a prime power. In particular, (q+1,6)--cages have been obtained from the projective planes of order q. Morever, infinite families of small regular graphs of girth 5 have been constructed performing algebraic operations on Fq. 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)--cages arising from the generalized quadrangles of order q, q a prime power.
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