Weak and strong domination in graphs

In a communication network, communication is needs to be reliable, fast and uninterrupted. Communication networks can be modeled with graphs. Vulnerability is the durability of the communication network against damage that may occur in a communication network. It is important that the communication network is not interrupted. For this reason, many studies on vulnerability have been made in graph theory and different measurements have been defined. In this thesis, the strong and weak dominations are studied which are important types of domination in graph theory. For some graph classes, the strong and weak domination numbers are calculated and the overall results obtained from the calculations are given with proofs. Throughout study, connected, undirected, simple graphs are studied. This thesis consists of five chapters. In the first chapter history of Graph Theory and its applications, some of vulnerability parameters which can be used in Graph Theory are explained. One of these parameters is domination, we mention about strong and weak domination numbers. We have also mention about the chess gave which is accepted as the beginning of domination concept in Graph Theory. In the second chapter, the basic definitions and theorems of graph theory are given in detail. In the third chapter, the concepts of domination, strong and weak domination are explained and an example is given with the materials and methods. In the fourth chapter, the results, theorems and proofs about the strong and weak domination number in path, cycles, complete, complete bipartite, power of cycle, power of path, comet, double comet, double star, comb, circular ladder, windmill, thorn rod, thorn star, thorn, theta, complete binary tree and complete k-ary tree graphs are given. In the fifth and the last chapter the results and recommendations of the study are given.