A small-world network derived from the deterministic uniform recursive tree by line graph operation**Supported by The Ministry of Science and Technology 973 project (No. 2010C B334708); National Science Foundation of China (Nos. 61164005, 11161037, 11101232, 11461054, 11551001); The Ministry of education scholars and innovation team support plan of Yangtze River (No. IRT1068); Qinghai Province Nature Science Foundation Project (Nos. 2012-Z-943,

Abstract

The deterministic uniform recursive tree is one of the deterministic versions of the uniform recursive tree . Zhang et al (2008 Eur. Phys. J. B 63 507–13) studied the properties of DURT, including its topological characteristics and spectral properties. Although DURT shows a logarithmic scaling with the size of the network, DURT is not a small-world network since its clustering coefficient is zero. Lu et al (2012 Physica A 391 87–92) proposed a deterministic small-world network by adding some edges with a simple rule in each DURT iteration. In this paper, we intoduce a method for constructing a new deterministic small-world network by the line graph operation in each DURT iteration. The line graph operation brings about cliques at each node of the previous given graph, and the resulting line graph possesses larger clustering coefficients. On the other hand, this operation can decrease the diameter at almost one, then giving the analytic solutions to several topological characteristics of the model proposed.