Generalized Recursive Circulant Graphs

Authors:
Shyue-Ming Tang;Yue-Li Wang;Chien-Yi Li
Affiliations:
National Defense University, Taipei City;National Taiwan University of Science and Technology, Taipei;National Taiwan University of Science and Technology, Taipei
Venue:
IEEE Transactions on Parallel and Distributed Systems
Year:
2012

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Dense bipartite circulants and their routing via rectangular twisted torus

Discrete Applied Mathematics

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Abstract

In this paper, we propose a new class of graphs called generalized recursive circulant graphs which is an extension of recursive circulant graphs. While retaining attractive properties of recursive circulant graphs, the new class of graphs achieve more flexibility in varying the number of vertices. Some network properties of recursive circulant graphs, like degree, connectivity and diameter, are adapted to the new graph class with more concise expression. In particular, we use a multidimensional vertex labeling scheme in generalized recursive circulant graphs. Based on the labeling scheme, a shortest path routing algorithm for the graph class is proposed. The correctness of the routing algorithm is also proved in this paper.