Using evolutionary algorithm for generation of dense families of circulant networks

Abstract

In this paper we consider the combinatorial optimization problem of the search for dense families of circulant networks with a good ratio between the order and diameter for a given degree. In particular, we distinguish the optimal families having the minimum possible diameter for a given degree and order of a graph. This work describes a new way of generation of analytical parametric descriptions of dense families of circulant networks using evolutionary algorithms. We present the families of circulants of degree 4 and 6 obtained by means of evolutionary algorithms. Some of these families of degree 6 improve previously known results.

Algebraic and computer-based methods in the undirected degree/diameter problem - A brief survey

“…In particular, for t = 2 and t = 3 they are called double-loop graphs and triple-loop graphs, respectively. According to [74], the maximum order of a triple-loop network C(n; {±1, ±s 2 , ±s 3 }) is: [73] used an evolutionary algorithm to find dense families of undirected circulant graphs. In particular, with the aid of this algorithm they found some families of large triple-loop graphs.…”