Research On Factional Matching Preclusion For Three Interconnections

With the development of information technology,the importance of interconnec-tion networks come into focus.However,it is inevitable that the processors of intercon-nection networks and the links between some processors may fail.Thus the stability of the interconnection networks have drawn considerable attention.As the topology of a interconnection network can be modeled as a graph,the graph theory becomes a powerful mathematical tool to study the stability of the interconnection networks.The matching preclusion involved in graph theory can be used as a measure of robustness in the event of edges failure in interconnection networks,so that The internet with a large matching preclusion number is considered to be more stable.The fractional matching is a generalization of matching,and has received much attention from many researchers.If the G=(V,E)is a simple undirected graph of order n.An edges subset F of G is a fractional matching preclusion set(FMP set for short)If G-F has no fraction perfect matching.The fractional matching preclusion number of G is the minimum size of FMP sets of G.An set F of edges and vertices of G is a is a fractional strong matching preclusion set(FSMP set for short)if G-F has no fraction perfect matching.The fractional strong matching preclusion number of G is the minimum size of FSMP sets of G.A FMP(FSMP)set of minimum cardinality is called optimal.The stability of three internationals are studied by using theory methods in this pa-per,that ia,to solve the problem of internet matching preclusion.The main conclusion are as follows:1.The strong matching preclusion number and fractional matching preclusion number of LT Q_nis n.Then the fractional strong matching preclusion number of 3-dimension,4-dimension,5-dimension and n-dimension Locally twisted cubes are cal-culated as 2,3,5 and n,respectively.In addition,all the optimal FSMP set of these graphs are discussed.2.The matching preclusion number,strong matching preclusion number and frac-tional matching preclusion number of CQ_nis n.Then the fractional strong matching preclusion number of 3-dimension,4-dimension,5-dimension and n-dimension Cross cubes are calculated as 2,3,5 and n,respectively.In addition,all the optimal FSMP set of these graphs are discussed.3.The matching preclusion number and fractional matching preclusion number of P(n,k)is 3.We obtained the fractional strong matching preclusion number of P(n,k)under different conditions is also 3 by further study and discussion.