Connectedness of graphs and its application to connected matroids through covering-based rough sets
This provides a novel theoretical framework for studying connectivity in graphs and matroids, which is incremental in linking these concepts through rough set theory.
The paper tackles the problem of analyzing graph connectedness using covering-based rough sets and extends this approach to matroids, showing that a matroid and its induced graph share the same connectedness property.
Graph theoretical ideas are highly utilized by computer science fields especially data mining. In this field, a data structure can be designed in the form of tree. Covering is a widely used form of data representation in data mining and covering-based rough sets provide a systematic approach to this type of representation. In this paper, we study the connectedness of graphs through covering-based rough sets and apply it to connected matroids. First, we present an approach to inducing a covering by a graph, and then study the connectedness of the graph from the viewpoint of the covering approximation operators. Second, we construct a graph from a matroid, and find the matroid and the graph have the same connectedness, which makes us to use covering-based rough sets to study connected matroids. In summary, this paper provides a new approach to studying graph theory and matroid theory.