The Matching Preclusion Number Of Arrangement Graphs And Two Cube Graphs

Science and technology develop fastly,there is a breakthrough takes place in the large computer systems,then promoting the social networks,we refer to graphs to represented by apex of the graph,and the physical connection between components are represented by edges.Internet topology refers to the connection mode between is determined by the correlation function,so it is good to make a wonderful interconnec-tion network topology,which will occur link failure and node failure to consider the network with fault element.The concept of matching preclusion number of graph G was proposed and it can be expressed by the function f that gives weight to each edge of graph G then the vertex satisfies?_e?vf(e)?1.If every vertex of graph G satisfies?_e?vf(e)=1,which is recorded as a perfect match.if other vertices satisfy?_e?vf(e)=1,with only one vertex satisfies?_e?v?f(e)=0,then it is called an almost perfect match of graph G.Matching exclusion set that an edge set F,which cause graph G-F not perfect match or almost perfect match,The minimum number of matching exclusion sets F is recorded as the matching exclusion number of graph G,if the vertex and edge set of graph G can be F,there is graph G-F.If there is neither perfect match nor almost perfect match,it is called graph G Strong match exclusion set,F is the minimum number and recorded as the strong matching exclusion number of graph G.If F is removed,graph G-F not have fractional perfect match.In this paper,we mainly study the related properties of arrangement Graph and get the smp(A_n,2)=2n-4.And each one the optimal matching exclusion set is trivial,that is,A_n,2is strongly super-matched,and the related structural characteristics of DH cube are obtained,f mp(DH(m,d,n))=n+1 and f smp(DH(m,d,n))=n+1 are given,and the exchange cube is analyzed,according to the structural characteristics of the cube graph,f mp(ECQ(s,t))=s+1 and f smp(ECQ(s,t))=s+1 are obtained.