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

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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 graph. 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 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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Acknowledgments

This work is supported in part by the National Natural Science Foundation of China under Grant Nos. 61170128, 61379049, and 61379089, the Science and Technology Key Project of Fujian Province, China, under Grant No. 2012H0043.

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Authors and Affiliations

  1. Tan Kah Kee College, Xiamen University, Zhangzhou, 363105, China

    Aiping Huang

  2. Lab of Granular Computing, Minnan Normal University, Zhangzhou, 363000, China

    William Zhu

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  1. Aiping Huang
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  2. William Zhu
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Correspondence to William Zhu.

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The authors declare that they have no financial and personal relationships with other people or organizations that can inappropriately influence their work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position.

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Communicated by A. Di Nola.

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Huang, A., Zhu, W. Connectedness of graphs and its application to connected matroids through covering-based rough sets. Soft Comput 20, 1841–1851 (2016). https://doi.org/10.1007/s00500-015-1859-2

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