Abstract
Computational intelligence and computer science rely on graph theory to solve combinatorial problems. Normal product and tensor product of an m-polar fuzzy graph have been introduced in this article. Degrees of vertices in various product graphs, like Cartesian product, composition, tensor product, and normal product, have been computed. Complement and μ-complement of an m-polar fuzzy graph are defined and some properties are studied. An application of an m-polar fuzzy graph is also presented in this article.
Highlights
Akram [1] introduced the notion of bipolar fuzzy graphs describing various methods of their construction as well as investigating some of their important properties
Rashmanlou et al [6] discussed some properties of bipolar fuzzy graphs and their results
We study the Cartesian product and composition of two m-polar fuzzy graphs and compute the degrees of the vertices in these graphs
Summary
Akram [1] introduced the notion of bipolar fuzzy graphs describing various methods of their construction as well as investigating some of their important properties. Ghorai and Pal [4] studied some operations and properties of an m-polar fuzzy graph. Rashmanlou et al [6] discussed some properties of bipolar fuzzy graphs and their results. We study the Cartesian product and composition of two m-polar fuzzy graphs and compute the degrees of the vertices in these graphs. The notions of normal product and tensor product of m-polar fuzzy graphs are introduced and some properties are studied. In the present work, we introduce the concept of complement, μcomplement of an m-polar fuzzy graph, and some properties are discussed. These concepts strengthen the decision-making in critical situations. Unless and otherwise specified, all graphs considered are m-polar fuzzy graphs
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