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Energy of Bipolar Fuzzy Graphs
2020In this chapter, we study the concept of energy of bipolar fuzzy graphs and present certain formulae, lower and upper bounds of Laplacian energy, signless Laplacian energy, dominating energy, out-dominating energy, double dominating energy, and double out-dominating energy of bipolar fuzzy graphs and bipolar fuzzy digraphs.
Muhammad Akram +2 more
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Domination in bipolar fuzzy soft graphs
Journal of Intelligent & Fuzzy SystemsThe concept of domination in graphs is very ancient. Several types of notions of domination in graphs have been discussed by many researchers. In this work, the concept of domination and some notions of domination sets, minimal dominating sets, independence sets, and maximal independence sets are introduced in bipolar fuzzy soft graphs.
Umair Amin +4 more
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Certain Types of Product Bipolar Fuzzy Graphs
International Journal of Applied and Computational Mathematics, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ghorai, Ganesh, Pal, Madhumangal
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Energy of double dominating bipolar fuzzy graphs
Journal of Applied Mathematics and Computing, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Muhammad Akram 0001 +2 more
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Characterization of regular bipolar fuzzy graphs
Afrika Matematika, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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2019
In this chapter, we present a novel frame work for handling bipolar fuzzy soft information by combining the theory of bipolar fuzzy soft sets with graphs. We present certain notions of bipolar fuzzy soft graphs. We investigate some of their properties. We discuss several applications of the bipolar fuzzy soft graphs in multiple criteria decision-making
Muhammad Akram, Fariha Zafar
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In this chapter, we present a novel frame work for handling bipolar fuzzy soft information by combining the theory of bipolar fuzzy soft sets with graphs. We present certain notions of bipolar fuzzy soft graphs. We investigate some of their properties. We discuss several applications of the bipolar fuzzy soft graphs in multiple criteria decision-making
Muhammad Akram, Fariha Zafar
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Creative Mathematics and Informatics, 2018
In this paper, we combine the concepts of bipolar fuzzy soft sets and graph theory. Then we introduce notations of bipolar fuzzy soft graph and strong bipolar fuzzy soft graph. We also present several different types of operations including cartesian product, strong product and composition on bipolar fuzzy soft graphs and investigate some properties of
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In this paper, we combine the concepts of bipolar fuzzy soft sets and graph theory. Then we introduce notations of bipolar fuzzy soft graph and strong bipolar fuzzy soft graph. We also present several different types of operations including cartesian product, strong product and composition on bipolar fuzzy soft graphs and investigate some properties of
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Application of Bipolar Fuzzy Sets in Planar Graphs
International Journal of Applied and Computational Mathematics, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Akram, Muhammad +2 more
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Special Types of Bipolar Fuzzy Graphs
2020In this chapter, we discuss the concept of irregularity in bipolar fuzzy graphs and present isomorphism properties of regular, m-totally regular, neighborly irregular, totally irregular, highly irregular, and neighborly totally irregular bipolar fuzzy graphs.
Muhammad Akram +2 more
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Bipolar felicitous fuzzy graphs
AIP Conference Proceedings, 2022T. Bharathi, S. Felixia
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