完全2-分图的l-边-连通度

The l-edge-connectivity of Complete Bipartite Graph

连通图G所谓的l-边-连通度(l-edge-connectivity),就是使图G成为至少l个分支所必须去掉的最少边数,记作λl(G),即λl(G)=min{|E′|∶E′■E(G),ω(G-E′)≥l}.研究了完全2-分图的l-边-连通度,得到了定理:设G=G[V1,V2]是一个完全2-分图,|V1|=r,|V2|=s,r+k=s,k≥0为整数.则图G的(k+2)-边-连通度为(k+1)r,即λk+2(G)=r(k+1).

For an integer l≥2, 1- edge- connectivity At（G） of a connected graph G of order p≥1 is the number of edges that need to be deleted from G to produce a disconnected graph with at least l components. In this note, the author investigates the l - edge - connectivity λl （G） of Complete Bipartite Graph and obtains some results. Suppose G = G[ V], V2 ] is a Complete Bipartite Graph, ｜ V1｜ = r, ｜ V2｜= s,r ＋ R = s,R ≥0 and k is integer, then （ k ＋ 2） - edge - connectivity of G graph is （ k ＋ 1 ） r, that is A （k ＋2） （G） = r（ k ＋ 1 ）.