Vague multigraphs

  • M. Baghernejad
  • R. A. BorzooeiEmail author
Methodologies and Application


A vague graph is a generalized structure of a fuzzy graph that gives more precision, flexibility and compatibility to a system when compared with systems that are designed using fuzzy graphs. In this paper, we applied the notion of vague sets to multigraphs and we introduce the concepts of vague multiset and Vague multigraph, which are two subclass of vague sets and vague graphs, respectively. Then we define the fundamental concepts of Vague multigraphs and get some related results. Moreover, by considering the notions of strength of edge, effective edge and effective vague multigraph, we investigate the planarity of a vague multigraph. Finally, we give an application for designing and modeling of streets in a city, by vague multigraphs.


Vague graph Vague multiset Vague multigraph Planarity of vague multigraph 



This study was funded by Shahid Beheshti University.

Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interest.

Human and animal rights

This article does not contain any studies with human participants or animals performed by any of the authors.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsIslamic Azad UniversityTehranIran
  2. 2.Department of MathematicsShahid Beheshti UniversityTehranIran

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