Comellas, Francesc; Miralles, Alicia Label-based routing for a family of scale-free, modular, planar and unclustered graphs. (English) Zbl 1226.05212 J. Phys. A, Math. Theor. 44, No. 20, Article ID 205102, 11 p. (2011). This paper discusses optimal labeling and routing for the family of self-similar, planar graphs with zero clustering introduced in the paper [A. Miralles, F. Comellas, L. Chen and Z. Zhang, “Planar unclustered graphs to model technological and biological networks,” Physica A 389, 1955–1664 (2010)]. In the earlier paper cited above, the authors introduced a family of graphs \(M_d(t)\) that are scale-free, small-world, modular, self-similar, and planar. The graphs are constructed inductively in \(t\) steps by adding \(d\) parallel paths to each edge whose end vertices were introduced in the previous step. Section 2 of the paper reviews the construction of \(M_d(t)\). Section 3 of the paper describes a way to label the vertices of \(M_d(t)\) for \(t \geq 0\) so that a routing by shortest paths between any two vertices can be found using just the labels on the vertices. Section 4 of the paper explains how to find a shortest path between any two vertices from the labels of the source and destination vertices. Reviewer: David E. Hurtubise (Altoona) Cited in 5 Documents MSC: 05C78 Graph labelling (graceful graphs, bandwidth, etc.) 05C10 Planar graphs; geometric and topological aspects of graph theory 05C38 Paths and cycles Keywords:planar graphs; unclustered graphs; label-based routing PDFBibTeX XMLCite \textit{F. Comellas} and \textit{A. Miralles}, J. Phys. A, Math. Theor. 44, No. 20, Article ID 205102, 11 p. (2011; Zbl 1226.05212) Full Text: DOI