A study on bipolar fuzzy graphs

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

doi:10.3233/ifs-141333

Cited by 134 publications

(42 citation statements)

References 22 publications

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“…( 2016a , b ), Rashmanlou and Pal ( 2013a , b ), Rashmanlou et al. ( 2015a , b , c ), Pramanik et al. ( 2016a , b ), Samanta and Pal ( 2011b , 2012b , 2015 , 2016 ) and Samanta et al.…”

Section: Introductionmentioning

confidence: 97%

A study on vague graphs

et al. 2016

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“…( 2016a , b ), Rashmanlou and Pal ( 2013a , b ), Rashmanlou et al. ( 2015a , b , c ), Pramanik et al. ( 2016a , b ), Samanta and Pal ( 2011b , 2012b , 2015 , 2016 ) and Samanta et al.…”

Section: Introductionmentioning

confidence: 97%

A study on vague graphs

et al. 2016

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“…Akram et al [5,6] introduced interval-valued fuzzy graph as an extension of fuzzy graph and established some of their properties. Moreover, some researchers applied fuzzy sets, intervalvalued fuzzy sets, intuitionistic fuzzy sets, vague sets and neutrosophic sets etc., on graphs [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. In 2012, Jun et al [23] combined the theory of the interval-valued fuzzy set with the fuzzy set, and introduced the notion of cubic set.…”

Section: Introductionmentioning

confidence: 99%

Cubic Graphs and Their Application to a Traffic Flow Problem

Muhiuddin¹,

Takallo²,

Jun³

et al. 2020

IJCIS

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A graph structure is a useful tool in solving the combinatorial problems in different areas of computer science and computational intelligence systems. In this paper, we introduce the concept of cubic graph, which is different from the notion of cubic graph in S. Rashid, N. Yaqoob, M. Akram, M. Gulistan, Cubic graphs with application, Int. J. Anal. Appl. 16 (2018), 733-750, and investigate some of their interesting properties. Then we define the notions of cubic path, cubic cycle, cubic diameter, strength of cubic graph, complete cubic graph, strong cubic graph and illustrate these notions by several examples. We prove that any cubic bridge is strong and we investigate equivalent condition for cubic cutvertex. Finally, we use the concept of cubic graphs in traffic flows to get the least time to reach the destination.

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“…Mathew et al [28] studied the energy of an FG. Rashmanlou et al [29][30][31][32] introduced some properties of FGs. Sunitha et al [33][34][35] presented new concepts for fuzzy graphs.…”

Section: Introductionmentioning

confidence: 99%

Certain Properties of Vague Graphs with a Novel Application

2020

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Fuzzy graph models enjoy the ubiquity of being present in nature and man-made structures, such as the dynamic processes in physical, biological, and social systems. As a result of inconsistent and indeterminate information inherent in real-life problems that are often uncertain, for an expert, it is highly difficult to demonstrate those problems through a fuzzy graph. Resolving the uncertainty associated with the inconsistent and indeterminate information of any real-world problem can be done using a vague graph (VG), with which the fuzzy graphs may not generate satisfactory results. The limitations of past definitions in fuzzy graphs have led us to present new definitions in VGs. The objective of this paper is to present certain types of vague graphs (VGs), including strongly irregular (SI), strongly totally irregular (STI), neighborly edge irregular (NEI), and neighborly edge totally irregular vague graphs (NETIVGs), which are introduced for the first time here. Some remarkable properties associated with these new VGs were investigated, and necessary and sufficient conditions under which strongly irregular vague graphs (SIVGs) and highly irregular vague graphs (HIVGs) are equivalent were obtained. The relation among strongly, highly, and neighborly irregular vague graphs was established. A comparative study between NEI and NETIVGs was performed. Different examples are provided to evaluate the validity of the new definitions. A new definition of energy called the Laplacian energy (LE) is presented, and its calculation is shown with some examples. Likewise, we introduce the notions of the adjacency matrix (AM), degree matrix (DM), and Laplacian matrix (LM) of VGs. The lower and upper bounds for the Laplacian energy of a VG are derived. Furthermore, this study discusses the VG energy concept by providing a real-time example. Finally, an application of the proposed concepts is presented to find the most effective person in a hospital.

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A study on bipolar fuzzy graphs

Cited by 134 publications

References 22 publications

A study on vague graphs

A study on vague graphs

Cubic Graphs and Their Application to a Traffic Flow Problem

Certain Properties of Vague Graphs with a Novel Application

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