Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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NEW CONCEPTS OF REGULAR INTERVAL-VALUED FUZZY GRAPHS

  • TALEBI, A.A. (Department of Mathematics, University of Mazandaran) ;
  • RASHMANLOU, HOSSEIN (Sama technical and vocatinal training college, Islamic Azad University) ;
  • DAVVAZ, BIJAN (Department of Mathematics, Yazd University)
  • Received : 2016.06.17
  • Accepted : 2016.07.11
  • Published : 2017.01.30
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Abstract

Recently, interval-valued fuzzy graph is a growing research topic as it is the generalization of fuzzy graphs. The interval-valued fuzzy graphs are more flexible and compatible than fuzzy graphs due to the fact that they allowed the degree of membership of a vertex to an edge to be represented by interval values in [0.1] rather than the crisp values between 0 and 1. In this paper, we introduce the concepts of regular and totally regular interval-valued fuzzy graphs and discusses some properties of the ${\mu}$-complement of interval-valued fuzzy graph. Self ${\mu}$-complementary interval-valued fuzzy graphs and self-weak ${\mu}$-complementary interval-valued fuzzy graphs are defined and a necessary condition for an interval valued fuzzy graph to be self ${\mu}$-complementary is discussed. We define busy vertices and free vertices in interval valued fuzzy graph and study their image under an isomorphism.

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References

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