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

Ali Asghar Talebi (), Seyed Hossein Sadati (), Hossein Rashmanlou and Ghulam Muhiuddin
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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

Chapter Chapter 25 in Fuzzy Optimization, Decision-making and Operations Research, 2023, pp 573-585 from Springer

Abstract: 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.

Keywords: Cubic fuzzy graph; Cubic strong edge; Dominating set; Strong vertex covering number; 05C99; 03E72 (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-35668-1_25

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DOI: 10.1007/978-3-031-35668-1_25

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