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.