Publication Date:
2018-09-18
Description:
Symmetry, Vol. 10, Pages 407: Vertex Labeling and Routing for Farey-Type Symmetrically-Structured Graphs Symmetry doi: 10.3390/sym10090407 Authors: Wenchao Jiang Yinhu Zhai Zhigang Zhuang Paul Martin Zhiming Zhao Jia-Bao Liu 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.
Electronic ISSN:
2073-8994
Topics:
Mathematics
,
Physics
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