Analysis of Road Map Design Based on Multigraph with Picture Fuzzy Information

Abstract

In this paper, the picture fuzzy planar graph is defined along with some basic properties of picture fuzzy graph. The notion of picture fuzzy planar graphs is introduced and the terms such as strong (weak) edges, strong (weak) picture fuzzy planar graphs, strength of an edge, degree of planarity, picture fuzzy faces, strong (weak) picture fuzzy faces, picture fuzzy dual graphs and picture fuzzy combinatorial dual graphs are defined. Some theorems on degree of planarity and picture fuzzy combinatorial dual graphs have been established. An application of picture fuzzy planar graph in the design of road maps is given.

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Acknowledgements

The authors are highly grateful to the learned reviewers for their valuable comments and suggestions to improve the quality of the article.

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Correspondence to Ganesh Ghorai.

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Das, S., Ghorai, G. Analysis of Road Map Design Based on Multigraph with Picture Fuzzy Information. Int. J. Appl. Comput. Math 6, 57 (2020). https://doi.org/10.1007/s40819-020-00816-3

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Keywords

  • Picture fuzzy graphs
  • Picture fuzzy planar graphs
  • Strong (weak) picture fuzzy planar graphs
  • Picture fuzzy dual graphs
  • Picture fuzzy combinatorial dual graph