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A study on vague graphs.

Hossein Rashmanlou1, Sovan Samanta2, Madhumangal Pal3

  • 1Young Researchers and Elite Club, Central Branch, Islamic Azad University, Tehran, Iran.

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|August 19, 2016
PubMed
Summary

This study introduces vague h-morphisms for vague graphs, exploring their properties on regular and strong regular vague graphs. New results on weak and co-weak isomorphisms are presented, alongside the definition of a complement for highly irregular vague graphs.

Keywords:
Highly irregular vague graphVague graphVague h-morphism

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Area of Science:

  • Graph Theory
  • Fuzzy Mathematics
  • Abstract Algebra

Background:

  • Vague graphs provide a more flexible framework than traditional fuzzy graphs.
  • Understanding structural properties and mappings in vague graph theory is crucial for applications.
  • Existing research lacks comprehensive studies on specific types of graph homomorphisms in vague settings.

Purpose of the Study:

  • To introduce and define the concept of vague h-morphism on vague graphs and regular vague graphs.
  • To investigate the behavior and properties of vague h-morphisms on vague strong regular graphs.
  • To derive significant results concerning weak and co-weak isomorphisms in the context of vague graphs.

Main Methods:

  • Definition of vague h-morphism and its application to different classes of vague graphs.
  • Analysis of the composition and properties of vague h-morphisms.
  • Derivation of isomorphism theorems tailored for vague graph structures.
  • Introduction of the [Formula: see text]-complement for highly irregular vague graphs.

Main Results:

  • Established the foundational properties of vague h-morphisms on vague and regular vague graphs.
  • Characterized the action of vague h-morphisms on vague strong regular graphs.
  • Derived key theorems on weak and co-weak isomorphisms for vague graphs.
  • Defined the [Formula: see text]-complement for highly irregular vague graphs, extending graph complement concepts.

Conclusions:

  • The introduction of vague h-morphisms provides a new tool for analyzing vague graph structures.
  • The study offers novel insights into the isomorphism properties within vague graph theory.
  • The defined [Formula: see text]-complement contributes to the understanding of irregular vague graph properties.