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Investigating Some Parameters of Cubic Fuzzy Graphs and an Application in Decision-Making Problem

In: Fuzzy Optimization, Decision-making and Operations Research

Author

Listed:
  • Ali Asghar Talebi

    (University of Mazandaran, Department of Mathematics)

  • Seyed Hossein Sadati

    (University of Mazandaran, Department of Mathematics)

  • Hossein Rashmanlou

    (University of Mazandaran, Department of Mathematics)

  • Ghulam Muhiuddin

    (University of Tabuk, Department of Mathematics)

Abstract

A cubic fuzzy graph stands as a fuzzy graph type with two fuzzy membership and interval-valued membership values which is a combination of two different fuzzy values that allows the ambiguous and uncertain variables modeling, where the same format expression is not feasible. In this research, we introduced two important parameters related to the vertices of a graph, i.e., the dominating set and vertex covering in a cubic fuzzy graph, and some of their features were considered. These concepts are developed on some special cubic fuzzy graphs. Accordingly, the domination and vertex covering numbers are shown as a real number. This has caused a better comparison in the results, and in addition, the effect of the resulting number has been seen to be the same in different memberships. Also, some features of dominating set and vertex covering have been studied in complete cubic fuzzy graph. Finally, an application of these concepts in a decision-making problem is presented.

Suggested Citation

  • Ali Asghar Talebi & Seyed Hossein Sadati & Hossein Rashmanlou & Ghulam Muhiuddin, 2023. "Investigating Some Parameters of Cubic Fuzzy Graphs and an Application in Decision-Making Problem," Springer Books, in: Chiranjibe Jana & Madhumangal Pal & Ghulam Muhiuddin & Peide Liu (ed.), Fuzzy Optimization, Decision-making and Operations Research, chapter 0, pages 573-585, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-35668-1_25
    DOI: 10.1007/978-3-031-35668-1_25
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