Some new large (Δ, 3)‐graphs

Abstract

We study the problem of finding large graphs with given degree and diameter D = 3; that is, the construction of graphs with number of vertices as large as possible for a given degree and diameter D = 3. There are two general methods to obtain large graphs: computer search and analytic methods. In this article, new ideas are proposed for analytic methods which allow us to improve the values for the entries (12,3), (13,3), and (14,3) in the table of the largest known ( , D)-graphs.