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

Authors:
Camino Balbuena;Yuqing Lin;Mirka Miller
Affiliations:
Departament de Matemítica Aplicada III, Universitat Politècnica de Catalunya, Campus Nord, Edifici C2, C/ Jordi Girona 1 i 3, E-08034 Barcelona, Spain;School of Electrical Engineering and Computer Science, The University of Newcastle, NSW 2308, Australia;School of Information Technology and Mathematical Sciences, University of Ballarat, Ballarat, Victoria 3353, Australia
Venue:
Discrete Applied Mathematics
Year:
2008

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Abstract

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 @k^'(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.