The optimal synchronizability of a class network

In this paper, to study the interaction between network structure and dynamical property in the context of synchronization, we analyze the relationship between synchronizability and topology structure of simple network graphs with N node and N+1 edges. An approach to construct the optimal synchronizability network of unweighted and undirected is presented. And, it is found that the class optimal synchronizability network structure with three chains. Every chain size is as same as possible, that is, maximum and minimum chain the difference between the number of nodes is less than or equal to 1. Moreover, the difference between maximum degree and minimum degree is less than or equal to 1 in this class network. At last, an example is given to illustration the process of construction optimal network.