Vulnerability of Subclasses of Chordal Graphs

In this paper, we introduce a new invariant that supports an accurate evaluation of the connectivity of graphs belonging to some subclasses of chordal graphs, allowing the establishment of a total ordering of the elements of the class. It is based on the minimal vertex separators of the graph, and, as so, its computation is performed in linear time. Results about the behavior of the new invariant and a comparison with the toughness are presented for block graphs.