Graph operation and its application to synthesis of interconnection networks and diagnosis of systems

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We studied on the synthesis and analysis of graphs for interconnection networks and fault diagnosis. We explain the results on graphs of de Bruijn family, fault diagnosis and product of graphs.1. Graph of de Bruijn family : decomposition of de Bruijn graphs by cycle rooted trees, determination of chromatic number and chromatic index, determination of domination number of generalized de Bruijn graphs, proposal of broadcasting algorithms.2. Fault diagnosis : necessary and sufficient condition for a network on Cayley graphs to be optimally diagnosable, proposal of fault diagnosis algorithm on butterfly networks by comparison approach, optimal diagnosis and constant round analysis of butterfly networks by adaptive fault diagnosis, proposal of (t,k) fault diagnosis and its characterization.3. Product of graphs : proposal of new graphs on Cayley graphs of wreath product of groups.