K-distance Domination Number Of Some Graphs

Graph theory is a branch of discrete mathematics, which is the theoretical foundation of modern computer. As an critical branch of discrete mathematics, graph theory plays an important role in theoretical and real world both. Graph theory has a long history of development. Since Euler’s Seven Bridges of Konigsberg is given for the first time, Graph theory has attracted a large number of scholars to attention and research. New issues are raised and addressed to graph theory development and brought a steady flow of power and pleasure. In this paper, some distance domination numbers of common graphs with simple structure are studied. Domination number is important for several applications in computer networks. It is the minimum number of vertices to dominate the whole network, i.e. minimum cost. The study of domination number is of great theoretical and practical significance. Bondage number is an important concept related to the domination number. It is a important indicator of network security performance. Distance domination number and distance bondage number is a classic natural extension of domination number and bondage number. They both have a broad realistic background and significance. But determination of distance domination numbers of a graph is a NPC problem. Therefore, it is particularly important to identify distance domination numbers. This can provide important reference for further determination of distance domination number and distance bondage number of other graphs with complex structures.The first chapter of this paper introduces the necessary basic concepts in graph theory, and realistic background of domination number.The chapter2determine some k-distance domination number of Cartesian product graph of paths, includes Pn, Pn×P2, Pn×P3, Pn×KmThe chapter3determine some k-distance domination number of Cartesian product graph of cycles, includes Cn, Cn×P>2, Cn×P3, Cn×Km.