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

A vertex-cut image is said to be a restricted cut of a graph image if it is a vertex-cut such that no vertex image in image has all its neighbors in image. Clearly, each connected component of image must have at least two vertices. The restricted connectivity image of a connected graph image 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.