Connectedness of graphs and its application to connected matroids through covering-based rough sets

Aiping Huang; William Zhu

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arXiv · 1312.4234

Connectedness of graphs and its application to connected matroids through covering-based rough sets

Aiping Huang·William Zhu

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Abstract

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.

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Aiping Huang, William Zhu. 2013-12-16. Connectedness of graphs and its application to connected matroids through covering-based rough sets. https://arxiv.org/abs/1312.4234

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