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

Fastest Distributed Consensus Problem on Fusion of Two Star Networks