Comparison Of Some Graphs The Number Of Spanning Tree And Network Reliability

Consider a network represented by a graph G with a probability of vertex failure p and a probability of edge failure q. The reliability of G, denoted by R(g), is theconnected probability of all vertices in G. The main aim of network reliability design is to find networks with maximum reliability with given number of vertices and edges. Results on network reliability design are very important and helpful for designing reliable network.In this thesis, we shall investigate several problems of reliable network.In chapter 1, after an introduction of the terminology and notations employed in this paper, we give a survey on number of a graph and overview of the main results of this thesis.In chapter 2, we mainly inverstigate the number of spanning trees of composition of graphs and obtain some new results.In chapter 3, the number of the cutsets of the graph is a very important index to the analysis and synthesis of reliable network. In this paper we compute the number of cutsets of edge of a specific graph using techniques from simple algebra, using the number of cutsets of edge of the graph comparing the reliable of twe networksIn chapter 4, we conclude the thesis by discussing some problems for further research.