Large networks with small diameter

Abstract

The construction of large networks with small diameter D for a given maximal degree Δ is a major goal in combinatorial network theory. Using genetic algorithms, together with Cayley graph techniques, new results for this degree/diameter problem can be obtained. A modification of the Todd-Coxeter algorithm yields further results and allows, with Sabidussi’s representation theorem, a uniform representation of vertex-symmetric graphs. The paper contains an updated table of the best known (A, Δ)-graphs and a table with the largest known graphs for a given Δ and maximum average distance μ between the nodes.