Generalized Petersen graphs are an important class of commonly used interconnection networks and have been studied . The total domination number of generalized Petersen graphs P(m,2) is obtained in this paper

We investigate the function for different networks based on complex network theory. In this paper, we choose five data sets from various areas to study. In the study of Chinese network, scale-free effect and hierarchical structure features are found in this complex system. These results indicate that the discovered features of Chinese character structure reflect the combination nature of Chinese characters. In addition, we study the community structure in Chinese character network. We can find that community structure is always considered as one of the most significant features in complex networks, and it plays an important role in the topology and function of the networks. Furthermore, we cut all the nodes in the different networks from low degree to high degree and then obtain many networks with different scale. According to the study, two interesting results have been obtained. First, the relationship between the node number of the maximum communities and the number of communities in the corresponding networks is studied and it is linear. Second, when the number of nodes in the maximum communities is increasing, the increasing tendency of the number of its edges slows down; we predict the complex networks have sparsity. The study effectively explains the characteristic and community structure evolution on different networks.

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In this paper we consider the total bondage number b t (G) for Generalized Petersen graphs, which is defined as the minimum number of edges whose removal results in a new graph with larger total domination number. This parameter measures to some extent the robustness of an interconnection network with respect to link failures. Generalized Petersen graphs are an important class of commonly used interconnection networks and have been studied recently. By constructing a family of minimum total dominating sets we compute the total bondage number of the Generalized Petersen graphs。

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