Notes on “Bipolar fuzzy graphs”

Yang, Hai-Long; Li, Shenggang; Yang, Wei; Lu, You

doi:10.1016/j.ins.2013.03.049

Cited by 90 publications

(24 citation statements)

References 20 publications

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“…Akram (2011Akram ( , 2013 worked on certain notions of bipolar fuzzy graphs. Further theory of bipolar fuzzy graphs was developed in Akram and Anam (2017), Akram and Sitara (2017), Akram and Sarwar (2017), Sarwar and , Singh and Kumar (2014a), Singh and Kumar (2014b) and Yang et al (2013). On the other hand, Dinesh and Ramakrishnan (2011) introduced the concept of the fuzzy graph structure.…”

Section: Introductionmentioning

confidence: 99%

Novel decision-making method based on bipolar neutrosophic information

2018

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Section: Introductionmentioning

confidence: 99%

Novel decision-making method based on bipolar neutrosophic information

2018

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“…Using these concepts many research is going on till date on bipolar fuzzy graphs such as Ghorai and Pal (2015b), Samanta and Pal (2012a, b, 2014), Yang et al. (2013). Chen et al.…”

Section: Introductionmentioning

confidence: 99%

Some isomorphic properties of m-polar fuzzy graphs with applications

Ghorai

Pal

2016

SpringerPlus

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The theory of graphs are very useful tool in solving the combinatorial problems in different areas of computer science and computational intelligence systems. In this paper, we present a frame work to handle m-polar fuzzy information by combining the theory of m-polar fuzzy sets with graphs. We introduce the notion of weak self complement m-polar fuzzy graphs and establish a necessary condition for m-polar fuzzy graph to be weak self complement. Some properties of self complement and weak self complement m-polar fuzzy graphs are discussed. The order, size, busy vertices and free vertices of an m-polar fuzzy graphs are also defined and proved that isomorphic m-polar fuzzy graphs have same order, size and degree. Also, we have presented some results of busy vertices in isomorphic and weak isomorphic m-polar fuzzy graphs. Finally, a relative study of complement and operations on m-polar fuzzy graphs have been made. Applications of m-polar fuzzy graph are also given at the end.

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“…Using this definition of bipolar fuzzy graphs, research is ongoing. Some work on bipolar fuzzy graphs may be found on [6,7,24,25,28,30]. Talebi and Rashmanlou [2] studied the complement and isomorphism of bipolar fuzzy graphs.…”

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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Notes on “Bipolar fuzzy graphs”

Cited by 90 publications

References 20 publications

Novel decision-making method based on bipolar neutrosophic information

Novel decision-making method based on bipolar neutrosophic information

Some isomorphic properties of m-polar fuzzy graphs with applications

On some operations and density of m-polar fuzzy graphs

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