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Paired Many-to-Many Disjoint Path Covers in Recursive Circulants $(G(2^m,4))$
Dec. 2013 (vol. 62 no. 12)
pp. 2468-2475
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.
Index Terms:
Fault tolerance,Multiprocessor interconnection,Electronic mail,Path planning,Data communication,recursive circulants,Fault tolerance,disjoint path covers,interconnection networks
Sook-Yeon Kim, Jung-Heum Park, "Paired Many-to-Many Disjoint Path Covers in Recursive Circulants $(G(2^m,4))$," IEEE Transactions on Computers, vol. 62, no. 12, pp. 2468-2475, Dec. 2013, doi:10.1109/TC.2012.133
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