A construction of small regular bipartite graphs of girth 8

Abstract

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.