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Fastest Distributed Consensus Problem on Fusion of Two Star Networks

Finding optimal weights for the problem of Fastest Distributed Consensus on networks with different topologies has been an active area of research for a number of years. Here in this work we present an analytical solution for the problem of Fastest Distributed Consensus for a network formed from fusion of two different symmetric star networks or in other words a network consists of two different symmetric star networks which share the same central node. The solution procedure consists of stratification of associated connectivity graph of network and Semidefinite Programming (SDP), particularly solving the slackness conditions, where the optimal weights are obtained by inductive comparing of the characteristic polynomials initiated by slackness conditions. Some numerical simulations are carried out to investigate the trade-off between the parameters of two fused star networks, namely the length and number of branches.