Preprint Article Version 1 This version is not peer-reviewed

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.

Journal reference: Symmetry 2018, 10, 407
DOI: 10.3390/sym10090407

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.

Subject Areas

complex networks; deterministic models; Farey-type graphs; vertex labeling; shortest path routing

Comments (0)

We encourage comments and feedback from a broad range of readers. See criteria for comments and our diversity statement.

Leave a public comment
Send a private comment to the author(s)
Views 0
Downloads 0
Comments 0
Metrics 0


×
Alerts
Notify me about updates to this article or when a peer-reviewed version is published.