Sufficient Conditions for Graphs to be λ′—Optimal and Super—λ′

Let G be a finite,simple and undirected graph.An edge-cut S of G is called a restricted edge-cut if G-S contains no isolated vertices.The minimum cardinality of all restrictededge-cuts is called the restricted connectivity of G,denoted by λ′(G).Let ξ(G)=min{d(x)+d(y)-2∶xy∈E(G)} be the minimum edge-degree of G.We call G λ′-optimal if λ′(G)=ξ(G) and super—λ′ if every minimum restricted edge-cut isolates an egeg.This paper shouws.Sufficient conditions for graphs to be λ′—optimal and super—λ′ are shoun by Fan-type condition