A construction of small regular bipartite graphs of girth 8
Let q be a prime a power and k an integer such that 3 <= k <= q. In this paper we present a method using Latin squares to construct adjacency matrices of k-regular bipartite graphs of girth 8 on 2 (kq(2) - q) vertices. Some of these graphs have the smallest number of vertices among the known regular graphs with girth 8.
girth latin squares incidence matrices cages