STP Approach to Formulate k-Externally Stable Sets of Graphs
作者单位：College of Agricultural Equipment EngineeringHenan University of Science and Technology College of Information EngineeringHenan University of Science and Technology College of Artificial IntelligenceNankai University
会议名称：《第40届中国控制会议》
会议日期：2021年
学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学]
关 键 词：STP Semi-tensor product of matrices k-ESS logical systems finite-valued systems matrix method
摘 要：In this paper the structure of graphs in terms of k-externally stable set（k-ESS） is investigated based on a new matrix product, called semi-tensor product of matrices. By defining an eigenvector and an eigenvalue of node subset of a graph, three necessary and sufficient conditions of k-ESS are proposed in a matrix form. Using these conditions, the concepts of k-ESS matrix are introduced. The k-ESS matrix provides the complete information of the corresponding structures of a graph. Further, an algorithm is designed to find all the structures of a graph by conducting a series of matrix operation. The proposed method and results may offer a new way to investigate the problems related to graph structures in the field of network systems.