In this talk, we will discuss a family of graphs related to
the high girth graphs D(k,q). The graphs D(k,q) were originally
constructed by utilizing a bilinear product based on the root system of an affine Lie algebra.? We give a modification of this
construction which applies to Generalized Kac-Moody algebras of rank 2. Using these constructions we obtain a new lower bound on the maximum number of edges in graphs without 14-cycles.? This is joint work with Art Terlep.