Certain Types of Product Bipolar Fuzzy Graphs

  • Ganesh Ghorai
  • Madhumangal Pal
Original Paper


Recently, bipolar fuzzy graph is a vastly growing research area as it is the generalization of the fuzzy graphs. In this paper, at first the concepts of regular and totally regular product bipolar fuzzy graphs is introduced. Then necessary and sufficient conditions are established under which regular and totally regular product bipolar fuzzy graph becomes equivalent. The notion of product bipolar fuzzy line graph is introduced and investigated some of its properties. A necessary and sufficient condition is given for a product bipolar fuzzy graph to be isomorphic to its corresponding product bipolar fuzzy line graph. It is also examined when an isomorphism between two product bipolar fuzzy graphs follows from an isomorphism of their corresponding fuzzy line graphs.


Bipolar fuzzy sets Product bipolar fuzzy graphs Regular product bipolar fuzzy graphs Totally regular product bipolar fuzzy graphs Product bipolar fuzzy line graphs 

Mathematics Subject Classification

05C72 05C76 



Financial support for the first author offered under the Innovative Research Scheme, UGC, New Delhi, India (Ref. No.VU/Innovative/Sc/15/2015) is thankfully acknowledged. The authors are thankful to the Editor-in-Chief and reviewers for their valuable comments and suggestions to improve the presentation of the paper.


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Copyright information

© Springer India Pvt. Ltd. 2015

Authors and Affiliations

  1. 1.Department of Applied Mathematics with Oceanology and Computer ProgrammingVidyasagar UniversityMidnaporeIndia

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