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

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

• Type: Journal
• Year: 2008
• Where: DAM
• Authors: Camino Balbuena, Yuqing Lin, Mirka Miller
• Keywords: Connected Graph, DAM 2008, Minimum Cardinality, Restricted Cut