• Journal of Communications and Networks
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• 제1권2호
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• pp.89-98
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• 1999

In a synchronization (sync) $network^1$containing N nodes, it is shown (Theorem 1c) that an arbitrarily connected sync network & is the union of a countable set of isolated connecting sync networks${&_i,i= 1,2,.., L}, I.E., & = \bigcup_{I=1}^L&_i$ It is shown(Theorem 2e) that aconnecting sync network is the union of a set of disjoint irreducible subnetworks having one or more nodes. It is further shown(Theorem 3a) that there exists at least one closed irreducible subnetwork in $&_i$. It is further demonstrated that a con-necting sync network is the union of both a master group and a slave group of nodes. The master group is the union of closed irreducible subnetworks in $&_i$. The slave group is the union of non-colsed irre-ducible subnetworks in $&_i$. The relationships between master-slave(MS), mutual synchronous (MUS) and hierarchical MS/MUS ent-works are clearly manifested [1]. Additionally, Theorem 5 shows that each node in the slave group is accessible by at least on node in the master group. This allows one to conclude that the synchro-nization information avilable in the master group can be reliably transported to each node in the slave group. Counting and combinatorial arguments are used to develop a recursive algorithm which counts the number $A_N$ of arbitrarily connected sync network architectures in an N-nodal sync network and the number $C_N$ of isolated connecting sync network in &. EXamples for N=2,3,4,5 and 6 are provided. Finally, network examples are presented which illustrate the results offered by the theorems. The notation used and symbol definitions are listed in Appendix A.