Minimum Boundary And Reliability Of Star Graph Networks

The topology of an interconnection network is generally modeled by an undirected graph G=(V,E).The network topology decides how well the processors could operate coordinately. For example, the higher the connectivity and edge connectivity are, the more reliable the interconnection network is. To provide some more accurate parameters for the study of the reliability of interconnection networks, some new parameters have been proposed. For example, extra (edge) connectivity are proposed and they are applied in many interconnection networks. The extra (edge) connectivity plays very important part in the research of many other reliability of interconnection. Boundary problem was proposed in order to study the reliability of the interconnection network in the further.Since Minimum boundary has been proposed, they played very important role both in theory and in proven of science and the application technology. It has become one of the tools researching the properties of many interconnected network. This article will mainly study the reliability of star graphs and we will use the minimum vertex boundary and minimum edge boundary. The article will get the following results, such as δ2(Sn)=2n-4; δ3(Sn=3n-7; δ4(Sn)=4n-10, and ζ2(Sn)=2n-4, ζ3(Sn)=3n-7, ζ4(Sn)=4n-10, ζ5(Sn)=5n-13for n≥3and κ1(Sn)=δ2(Sn)=2n-4for n≥5, K2(Sn)=δ3(Sn)=3n-7for n≥6.