Embedding of fuzzy graphs on topological surfaces

  • Shriram Kalathian
  • Sujatha Ramalingam
  • Narasimman Srinivasan
  • Sundareswaran Raman
  • Said Broumi
Original Article


Planar graph is a special type in crisp as well as in fuzzy graphs. In fuzzy planar graphs, the planarity value is the amount of planarity of the crossed fuzzy edges, so that the intersection of fuzzy edges are possible in fuzzy graphs as compared to the planar graphs in crisp. Generally, the fuzzy planar graphs are depicted in the plane surface. In this paper, the embedding of fuzzy graphs are discussed in the surfaces like sphere and m-torus. Moreover, definition of fuzzy planar triangulation, straight-line, and piecewise embedding are also stated for planar embedding. Some of the effective definitions and theorems are illustrated with examples. Theorems like Euler’s formula for plane and sphere surfaces are proved and formulated for fuzzy planar graphs.


Fuzzy graphs Planar embedding Sphere embedding m-Torus embedding Total fuzzy face value Fuzzy planar triangulation 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  • Shriram Kalathian
    • 1
  • Sujatha Ramalingam
    • 1
  • Narasimman Srinivasan
    • 1
  • Sundareswaran Raman
    • 1
  • Said Broumi
    • 2
  1. 1.Department of MathematicsSSN College of EngineeringChennaiIndia
  2. 2.Laboratory of Information Processing, Faculty of Science Ben MSikUniversity Hassan IICasablancaMorocco

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