Diameter-sufficient conditions for a graph to be super-restricted connected

A vertex-cut XX is said to be a restricted cut of a graph GG if it is a vertex-cut such that no vertex uu in GG has all its neighbors in XX. Clearly, each connected component of G−XG−X must have at least two vertices. The restricted connectivity κ′(G)κ′(G) of a connected graph GG is defined as the minimum cardinality of a restricted cut. Additionally, if the deletion of a minimum restricted cut isolates one edge, then the graph is said to be super-restricted connected. In this paper, several sufficient conditions yielding super-restricted-connected graphs are given in terms of the girth and the diameter. The corresponding problem for super-edge-restricted-connected graph is also studied.