The Twin Domination Number And Out-domination Number Of Several Kinds Of Digraphs

With the rapid development of computer technology, graph theory which is an important part of discrete mathematics, has been developed rapidly, and more and more widely used.The theory of the domination number of a graph is an important research direction in graph theory, it has been widely applied to communication network, monitoring system and many other areas. For example, a network must consider the communication efficiency, save the communication resources, timely diagnosis of the disorder, which requires us in the network looking for some central node, through the central control node to control the whole situation and network. So how do we choose the central nodes. And node as little as possible to control the situation so that each node can communicate directly with the adjacent central node. Therefore, the domination theory has become a hot research in graph theory.Through the research, it is found that some classes of graphs. For example, Cartesian product, strong product, lexicographic product, are graphs obtained by some simple graphs with special structure. The research about the twin domination number and out-domination number of those graphs has been provided a scientific solving methods for effective nets.This paper mainly studies the twin domination number and out-domination number of some special classes of graphs.The text of the paper consists of three chapters:In the first chapter, we introduce the background of domination number, and give definitions of cartesian product, strong product and lexicographic product, etc. Finally, we introduce contents and main result in this paper.In the second chapter, according to the definition of twin domination number, we obtain the twin domination number of Cm Cn, where m = 2, 3, 4, 5, 6; secondly, we obtain the twin domination number of Cm? Cnand Cm? Pn; finally, we obtain the twin domination number of lexicographic product of some digraphs.In the third chapter, we first study the background of out-domination number of some digraphs. Finally, we mainly give out-domination number of lexicographic product of some digraphs.