Issue No. 12 - Dec. (2013 vol. 62)
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TC.2012.133
Sook-Yeon Kim , Hankyong National University, Korea
Jung-Heum Park , The Catholic University of Korea, Korea
A disjoint path cover (DPC for short) of a graph is a set of disjoint paths that cover all the vertices of the graph. A paired many-to-many $(k)$-DPC is a DPC composed of $(k)$ paths between $(k)$ sources and $(k)$ sinks, such that each source is joined to a designated sink. We show that recursive circulant $(G(2^m,4))$ with at most $(f)$ faulty vertices and/or edges being removed has a paired many-to-many $(k)$-DPC joining $(k)$ arbitrary sources and sinks for any $(f)$ and $(k \ge 2)$, subject to $(f+2k \le m+1)$, where $(m \ge 5)$. The bound $(m+1)$ on $(f+2k)$ is the best possible.
Fault tolerance, Multiprocessor interconnection, Electronic mail, Path planning, Data communication
S. Kim and J. Park, "Paired Many-to-Many Disjoint Path Covers in Recursive Circulants $(G(2^m,4))$," in IEEE Transactions on Computers, vol. 62, no. 12, pp. 2468-2475, 2013.