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Regular bipolar fuzzy graphs

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Abstract

We introduce the concepts of regular and totally regular bipolar fuzzy graphs. We prove necessary and sufficient condition under which regular bipolar fuzzy graph and totally bipolar fuzzy graph are equivalent. We introduce the notion of bipolar fuzzy line graphs and present some of their properties. We state a necessary and sufficient condition for a bipolar fuzzy graph to be isomorphic to its corresponding bipolar fuzzy line graph. We examine when an isomorphism between two bipolar fuzzy graphs follows from an isomorphism of their corresponding bipolar fuzzy line graphs.

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Acknowledgments

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

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Authors and Affiliations

  1. Punjab University College of Information Technology, University of the Punjab, Old Campus, Lahore, 54000, Pakistan

    Muhammad Akram

  2. Institute of Mathematics and Computer Science, Wroclaw University of Technology, Wyb. Wyspianskiego 27, 50-370, Wrocław, Poland

    Wieslaw A. Dudek

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  1. Muhammad Akram
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  2. Wieslaw A. Dudek
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Correspondence to Muhammad Akram.

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Akram, M., Dudek, W.A. Regular bipolar fuzzy graphs. Neural Comput & Applic 21 (Suppl 1), 197–205 (2012). https://doi.org/10.1007/s00521-011-0772-6

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