On partitionable, confidentially connected and unbreakable graphs
نویسندگان
چکیده
Some problems related to security in communication networks lead to consider a new type of connectivity in graphs, namely the confidential connectivity. In this paper we present a characterization of unbreakable graphs using the notion of weak decomposition and we give some applications of minimal unbreakable graphs. In fact, we showed that a graph G is confidentially connected if and only if it does not have a star cutset. We also showed that a minimal imperfect graph does not have a star cutset. We gave a constructive proof of the fact that every (α, ω)-partitionable graph is confidentially connected, for a superclass of minimal imperfect graphs.
منابع مشابه
Structural properties of recursively partitionable graphs with connectivity 2
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