Vertex Labeling and Routing for Farey-Type Symmetrically-Structured Graphs
by
Wenchao Jiang 1, Yinhu Zhai 2, Zhigang Zhuang 1, Paul Martin 3, Zhiming Zhao 3
and Jia-Bao Liu 4,*
and Jia-Bao Liu 4,*
1
School of Computer, Guangdong University of Technology, Guangzhou 510006, China
2
School of Information Engineering, Guangdong University of Technology, Guangzhou 510006, China
3
System and Network Engineering Research Group, Informatics Institute, University of Amsterdam, Science Park 904, 1098XH Amsterdam, The Netherlands
4
School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China
*
Author to whom correspondence should be addressed.
Symmetry 2018, 10(9), 407; https://doi.org/10.3390/sym10090407
Received: 31 July 2018 / Revised: 13 September 2018 / Accepted: 15 September 2018 / Published: 17 September 2018
(This article belongs to the Special Issue Symmetry in Computing Theory and Application)
The generalization of Farey graphs and extended Farey graphs all originate from Farey graphs. They are simultaneously scale-free and small-world. A labeling of the vertices for them are proposed here. All of the shortest paths between any two vertices in these two graphs can be determined only on their labels. The number of shortest paths between any two vertices is the product of two Fibonacci numbers; it is increasing almost linearly with the order or size of the graphs. However, the label-based routing algorithm runs in logarithmic time O(logn). Our efficient routing protocol for Farey-type models should help contribute toward the understanding of several physical dynamic processes.
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Keywords:
complex networks; deterministic models; Farey-type graphs; vertex labeling; shortest path routing
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MDPI and ACS Style
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.
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