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Application of Bipolar Fuzzy Sets in Planar Graphs

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Abstract

A bipolar fuzzy set is a generalization of a fuzzy set. In this paper, we apply the concept of bipolar fuzzy sets to multigraphs and planar graphs. We introduce the notions of bipolar fuzzy multigraphs, bipolar fuzzy planar graphs, bipolar fuzzy dual graphs, and investigate some of their interesting properties. We also study isomorphism between bipolar fuzzy planar graphs.

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Acknowledgments

The authors are highly thankful to the referees for their valuable comments and suggestions.

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Authors and Affiliations

  1. Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan

    Muhammad Akram

  2. Department of Mathematics, JKHS, Tamluk, India

    Sovan Samanta

  3. Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, 721 102, India

    Madhumangal Pal

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  1. Muhammad Akram
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  2. Sovan Samanta
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  3. Madhumangal Pal
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Correspondence to Muhammad Akram.

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Akram, M., Samanta, S. & Pal, M. Application of Bipolar Fuzzy Sets in Planar Graphs. Int. J. Appl. Comput. Math 3, 773–785 (2017). https://doi.org/10.1007/s40819-016-0132-4

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  • DOI: https://doi.org/10.1007/s40819-016-0132-4

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