ON THE EXISTENCE OF THE h-RESTRICTED EDGE CONNECTIVITY OF A GRAPH

IntroductionLet G=(V,E) be a finite,simple and undi-rected graph with vertex set V and edge set E.We' ll follow the terminology and notation of Ref.1 ]and terms not defined here can be found inRefs.1 ,2 ].A set S of edges of G is called an edgedisconnecting set if G - S is disconnected. Theusual edge connectivityλ(G) of G is the minimumcardinality over the all edge disconnecting sets ofG.Note that,in the above definition,absolutelyno conditions or restrictions are imposed either onthe…

ON THE EXISTENCE OF THE h-RESTRICTED EDGE CONNECTIVITY OF A GRAPH

Let h be a nonnegative integer. The h-restricted edge connectivity λh(G) of a simple connected graph G is defined as the minimum cardinality over the sets of edges of G, if any, whose removal disconnects G and every component of the resulting graph has more than h vertices. This paper gave a necessary and sufficient condition and also three useful sufficient conditions to guarantee the existence of λh(G). Moreover, it explicitly characterized the graphs whose 2-restricted edge connectivities do not exist.