Degree conditions for restricted-edge-connectivity and isoperimetric-edge-connectivity to be optimal

For a connected graph G=(V,E), an edge set S⊂E is a k-restricted-edge-cut, if G-S is disconnected and every component of G-S has at least k vertices. The k-restricted-edge-connectivity of G, denoted by λk(G), is defined as the cardinality of a minimum k-restricted-edge-cut. The k-isoperimetric-edge-connectivity is defined as γk(G)=min{|[U,U¯]|:U⊂V,|U|⩾k,|U¯|⩾k}, where [U,U¯] is the set of edges with one end in U and the other end in U¯=V⧹U. In this note, we give some degree conditions for a graph to have optimal λk and/or γk.