Research On Liar Domination And Distance Paired Domination In Generalized Petersen Graph

The domination of graphs is well applied in computer network, for example, graph G could denote a computer network, and each vertex in V(G) could denote a processor. And the sides of graph G denote the neighborhood of equipments or the processors which have line connection. Equipment areas are denoted by every vertices in the graph respectively. Thus, the problem of disposable devices in network is converted to the the domination of graphs.Liar domination was first introduced by P.J.Slater, and Joanna Raczek generalized the concept of k-distance paired domination, these are well studied recently. In view of the significance of Peterson graphs, the author proves the general law of Liar domination and k-distance paired domination set based on the generalized Peterson graphs according to the the results of previous studies. Then, I also study the relationship of them, and give the exact value in some conditions. Main conclusions are as follows:(1) we study the Liar domination number of generalized Peterson graphs P(n,1) and P(n,2), and the conclusions are as follows, i(2) we study the k-distance domination number of generalized Peterson graphs P(n,1) and P(n,2), and the conclusions are as follows, otherwise.