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Interval-valued fuzzy planar graphs

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Abstract

In this paper, interval-valued fuzzy planar graphs are defined and several properties are studied. The interval-valued fuzzy graphs are more efficient than fuzzy graphs, since the degree of membership of vertices and edges lie within the interval [0, 1] instead at a point in fuzzy graphs. We also use the term ‘degree of planarity’ to measures the nature of planarity of an interval-valued fuzzy graph. The other relevant terms such as strong edges, interval-valued fuzzy faces, strong interval-valued fuzzy faces are defined here. The interval-valued fuzzy dual graph which is closely associated to the interval-valued fuzzy planar graph is defined. Several properties of interval-valued fuzzy dual graph are also studied. An example of interval-valued fuzzy planar graph is given.

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Acknowledgments

We would like to thank the anonymous referees, Associate Editor and Editor-in-Chief for their valuable comments and also express appreciation of their constructive suggestions to improve the paper.

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Authors and Affiliations

  1. Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, 721102, India

    Tarasankar Pramanik, Sovan Samanta & Madhumangal Pal

Authors
  1. Tarasankar Pramanik
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  2. Sovan Samanta
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  3. Madhumangal Pal
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Correspondence to Sovan Samanta.

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Pramanik, T., Samanta, S. & Pal, M. Interval-valued fuzzy planar graphs. Int. J. Mach. Learn. & Cyber. 7, 653–664 (2016). https://doi.org/10.1007/s13042-014-0284-7

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  • DOI: https://doi.org/10.1007/s13042-014-0284-7

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