Regularity of vague graphs

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

doi:10.3233/ifs-162114

Cited by 43 publications

(31 citation statements)

References 14 publications

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“…Akram et al [8][9][10][11][12][13][14] presented new definitions of FGs. Borzooei and Rashmanlou [15][16][17][18] investigated different concepts on VG. Gani and Radha [19] recommended RFGsand TRFGs.…”

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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Section: Introductionmentioning

confidence: 99%

Certain Properties of Vague Graphs with a Novel Application

2020

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“…al [13], and Borzooei [14] presented much work in the domain of the fuzzy graph and its several applications in real life. Samanta and Pal [6] and Rashmanlou and Pal [15] presented the concept of the irregular and regular fuzzy graph. They also described some applications of those graphs.…”

Section: Introductionmentioning

confidence: 99%

“…The neutrosophic graph [12] can efficiently model the inconsistent information about any real-life problem. Recently, many researchers have more actively worked on neutrosophic graph theory; for instance, Ye [29], Yang et al [30], Naz et al [31], Broumi [15], and Arkam [32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

A Study of Regular and Irregular Neutrosophic Graphs with Real Life Applications

Huang

et al. 2019

Mathematics

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Fuzzy graph theory is a useful and well-known tool to model and solve many real-life optimization problems. Since real-life problems are often uncertain due to inconsistent and indeterminate information, it is very hard for an expert to model those problems using a fuzzy graph. A neutrosophic graph can deal with the uncertainty associated with the inconsistent and indeterminate information of any real-world problem, where fuzzy graphs may fail to reveal satisfactory results. The concepts of the regularity and degree of a node play a significant role in both the theory and application of graph theory in the neutrosophic environment. In this work, we describe the utility of the regular neutrosophic graph and bipartite neutrosophic graph to model an assignment problem, a road transport network, and a social network. For this purpose, we introduce the definitions of the regular neutrosophic graph, star neutrosophic graph, regular complete neutrosophic graph, complete bipartite neutrosophic graph, and regular strong neutrosophic graph. We define the d m - and t d m -degrees of a node in a regular neutrosophic graph. Depending on the degree of the node, this paper classifies the regularity of a neutrosophic graph into three types, namely d m -regular, t d m -regular, and m-highly irregular neutrosophic graphs. We present some theorems and properties of those regular neutrosophic graphs. The concept of an m-highly irregular neutrosophic graph on cycle and path graphs is also investigated in this paper. The definition of busy and free nodes in a regular neutrosophic graph is presented here. We introduce the idea of the μ -complement and h-morphism of a regular neutrosophic graph. Some properties of complement and isomorphic regular neutrosophic graphs are presented here.

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“…Samanta and Pal defined fuzzy tolerance graphs [32], fuzzy threshold graphs [36], fuzzy planar graphs [38], fuzzy k-competition graphs and p-competition fuzzy graphs [34], irregular bipolar fuzzy graphs [35]. Borzooei and Rashmanlou [6][7][8][9][10][11][12] investigated new concepts on vague graphs. In this paper, we present the concepts of neighbourly irregular interval-valued fuzzy graphs, neighbourly totally irregular interval-valued fuzzy graphs, highly irregular interval -valued fuzzy graphs, and highly totally irregular interval-valued fuzzy graphs are introduced and investigated.…”

Section: Introductionmentioning

confidence: 99%

New Concepts of Interval-Valued Fuzzy Graphs with Application

Rashmanlou¹,

Jouybari²

2017

JMI

Self Cite

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Abstract. Concepts of graph theory are applied in many areas of computer science including image segmentation, data mining, clustering, image capturing and networking. Fuzzy graph theory is successfully used in many problems, to handle the uncertainty that occurs in graph theory. An interval-valued fuzzy 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, new concepts of irregular interval-valued fuzzy graphs such as neighbourly totally irregular intervalvalued fuzzy graph, highly irregular interval-valued fuzzy graphs and highly totally irregular interval-valued fuzzy graphs are introduced and investigated. A necessary and sufficient condition under which neighbourly irregular and highly irregular intervalvalued fuzzy graphs are equivalent is discussed.

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Regularity of vague graphs

Cited by 43 publications

References 14 publications

Certain Properties of Vague Graphs with a Novel Application

Certain Properties of Vague Graphs with a Novel Application

A Study of Regular and Irregular Neutrosophic Graphs with Real Life Applications

New Concepts of Interval-Valued Fuzzy Graphs with Application

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