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Vertex Labeling and Routing for Farey-Type Symmetrically-Structured Graphs
Version 1
: Received: 31 July 2018 / Approved: 1 August 2018 / Online: 1 August 2018 (08:36:16 CEST)
A peer-reviewed article of this Preprint also exists.
Jiang, W.; Zhai, Y.; Zhuang, Z.; Martin, P.; Zhao, Z.; Liu, J.-B. Vertex Labeling and Routing for Farey-Type Symmetrically-Structured Graphs. Symmetry 2018, 10, 407. Jiang, W.; Zhai, Y.; Zhuang, Z.; Martin, P.; Zhao, Z.; Liu, J.-B. Vertex Labeling and Routing for Farey-Type Symmetrically-Structured Graphs. Symmetry 2018, 10, 407.
Abstract
The generalization of Farey graphs and extended Farey graphs are all originated from Farey graph and scale-free and small-world simultaneously. We propose a labeling of the vertices for it that allows determining all the shortest paths routing between any two vertices only based on their labels. The maximum number of shortest paths between any two vertices is huge as the product of two Fibonacci numbers, however, the label-based routing algorithm runs in linear time O(n). The existence of an efficient routing protocol for Farey-type models should help the understanding of several physical dynamic processes on it.
Keywords
complex networks; deterministic models; Farey-type graphs; vertex labeling; shortest path routing
Subject
Computer Science and Mathematics, Computer Vision and Graphics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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