Vertex labeling and routing in self-similar outerplanar unclustered graphs modeling complex networks

This paper introduces a labeling and optimal routing algorithm for a family of modular, self-similar, small-world graphs with clustering zero. Many properties of this family are comparable to those of networks associated with technological and biological systems with low clustering, such as the power grid, some electronic circuits and protein networks. For these systems, the existence of models with an efficient routing protocol is of interest to design practical communication algorithms in relation to dynamical processes (including synchronization) and also to understand the underlying mechanisms that have shaped their particular structure.