Graph Models for Security Monitoring of Streets and Balance Communication of WSNs

The concepts of k-degree and k-balance control sets of graphs are abstracted from some real-world problems such as the location of cameras for saving resources in street security monitoring and the arrangement of major sensors for balancing load in wireless sensor networks. Then using a new matrix analysis tool, semi-tensor product of matrices (STP) developed in recent years, such two kinds of control sets are formulated by establishing a necessary and sufficient conditions that determine whether or not a vertex subset of a graph is a k-degree control set, and a necessary condition that facilitates finding k-balance control sets of a graph. Finally the effectiveness of the idea and the correctness of the results are verified by studying security monitoring of a street.