Bipolar Fuzzy Graphs with Categorical Properties

Rashmanlou, Hossein; Samanta, Sovan; Pal, Madhumangal; Borzooei, Rajab Ali

doi:10.1080/18756891.2015.1063243

Cited by 97 publications

(34 citation statements)

References 22 publications

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“…Talebi and Rashmanlou [2] studied the complement and isomorphism of bipolar fuzzy graphs. Rashmanlou et al [19,20] studied bipolar fuzzy graphs and bipolar fuzzy graphs with categorical properties.…”

Section: Introductionmentioning

confidence: 99%

On some operations and density of m-polar fuzzy graphs

Ghorai

Pal

2015

Pacific Science Review A: Natural Science and Engineering

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a b s t r a c tThe theoretical concepts of graphs are highly utilized by computer science applications, social sciences, and medical sciences, especially in computer science for applications such as data mining, image segmentation, clustering, image capturing, and networking. Fuzzy graphs, bipolar fuzzy graphs and the recently developed m-polar fuzzy graphs are growing research topics because they are generalizations of graphs (crisp). In this paper, three new operations, i.e., direct product, semi-strong product and strong product, are defined on m-polar fuzzy graphs. It is proved that any of the products of m-polar fuzzy graphs are again an m-polar fuzzy graph. Sufficient conditions are established for each to be strong, and it is proved that the strong product of two complete m-polar fuzzy graphs is complete. If any of the products of two m-polar fuzzy graphs G 1 and G 2 are strong, then at least G 1 or G 2 must be strong. Moreover, the density of an m-polar fuzzy graph is defined, the notion of balanced m-polar fuzzy graph is studied, and necessary and sufficient conditions for the preceding products of two m-polar fuzzy balanced graphs to be balanced are established. Finally, the concept of product m-polar fuzzy graph is introduced, and it is shown that every product m-polar fuzzy graph is an m-polar fuzzy graph. Some operations, like union, direct product, and ring sum are defined to construct new product m-polar fuzzy graphs.

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Section: Introductionmentioning

confidence: 99%

On some operations and density of m-polar fuzzy graphs

Ghorai

Pal

2015

Pacific Science Review A: Natural Science and Engineering

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“…Mordeson and Peng [5] defined join, union, Cartesian product, and composition of two fuzzy graphs. Rashmanlou et al [6] discussed some properties of bipolar fuzzy graphs and their results. Sunitha and Vijaya Kumar [7] defined the complement of a fuzzy graph in another way which gives a better understanding about that concept.…”

Section: Introductionmentioning

confidence: 99%

Vertex Degrees and Isomorphic Properties in Complement of an m-Polar Fuzzy Graph

Ramprasad¹,

Varma²,

Satyanarayana³

et al. 2017

Advances in Fuzzy Systems

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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.

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“…Borzooei et al [2] defined domination in vague graphs. Rashmanlou et al [8,9,10,11,12,13,14,15,16] invetigated some basic results on bipolar fuzzy graphs and vague graphs. In this paper, we study some results on point set dominating set and its number of vague graphs and semi complete vague graph.…”

Section: Introductionmentioning

confidence: 99%

A Study on Domination Sets in Vague Graphs with Novel Applications

Rashmanlou¹,

Lakdashti²,

Sabet³

2018

APAM

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Abstarct. Theoretical concepts of graphs are highly utilized by computer science applications. Especially in research areas of computer science such as data mining, image segmentation, clustering, image capturing and networking. Fuzzy graph theory has numerous applications in modern sciences and technology such as neural networks, artificial intelligence and decision making. A vague graph is a generalized structure of a fuzzy graph that gives more precision, flexibility, and compatibility to a system when compared with systems that are designed using fuzzy graphs. In this paper, we study some results on point set dominating set and its number of vague graphs and semi complete vague graphs. Likewise, we introduce the bounds with other domination parameters of vague graphs. Finally, we give some applications of point set dominating sets in the other sciences.

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Bipolar Fuzzy Graphs with Categorical Properties

Cited by 97 publications

References 22 publications

On some operations and density of m-polar fuzzy graphs

On some operations and density of m-polar fuzzy graphs

Vertex Degrees and Isomorphic Properties in Complement of an m-Polar Fuzzy Graph

A Study on Domination Sets in Vague Graphs with Novel Applications

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