A study on vague graphs

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

doi:10.1186/s40064-016-2892-z

Cited by 20 publications

(8 citation statements)

References 16 publications

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“…Borzooei and Rashmanlou [30][31][32][33][34] analyzed new concepts of VGs. Rashmanlou et al [35][36][37][38][39][40] investigated new results in VGs. Ghorai and Pal [41] studied regular product vague graphs and product vague line graphs.…”

Section: Introductionmentioning

confidence: 99%

Novel Concepts of Domination in Vague Graphs with Application in Medicine

Qiang

Akhoundi

Kou

et al. 2021

Mathematical Problems in Engineering

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VG can manage the uncertainty relevant to the inconsistent and indeterminate information of all real-world problems, in which FGs possibly will not succeed in bringing about satisfactory results. The previous definitions’ restrictions in FGs have made us present new definitions in VGs. A wide range of applications have been attributed to the domination in graph theory for several fields such as facility location problem, school bus routing, modeling biological networks, and coding theory. Therefore, in this research, we study several concepts of domination, such as restrained dominating set (RDS), perfect dominating set (PDS), global restrained dominating set (GRDS), total k -dominating set, and equitable dominating set (EDS) in VGs and also introduce their properties by some examples. Finally, we try to represent the application and importance of domination in the field of medical science and discuss the topic in today’s world, namely, the corona vaccine.

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Section: Introductionmentioning

confidence: 99%

Novel Concepts of Domination in Vague Graphs with Application in Medicine

Qiang

Akhoundi

Kou

et al. 2021

Mathematical Problems in Engineering

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“…Several mathematicians, such as Rashmanlou and Pal [7], Samanta and Pal [8], Ghorai and Pal [9], Paramik et al . [10], Rashmanlou et al [11, 12], Nandhini and Nandhini [13], and Borzooei et al . [14] have researched a lot in the area of the fuzzy graph and its applications in real‐life problems.…”

Section: Introductionmentioning

confidence: 99%

Study on neutrosophic graph with application in wireless network

Yao

2020

CAAI trans. intell. technol.

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A neutrosophic network is an extension of an intuitionistic fuzzy network that provides more precision compatibility and flexibility than an intuitionistic fuzzy graph in structuring and modelling many real‐life problems. The authors have explored the use of a neutrosophic network for modelling the passive optical network, mobile ad hoc network (MANET), and wireless sensor graph. They have presented the idea of strong arc, weak arc strong domination numbers, and strong perfect domination of neutrosophic network. They have described the method to find the values of strong and strong perfect domination of neutrosophic network. Finally, they use the idea of a strong arc strong domination number in MANET and wireless sensor graphs.

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“…Gani and Radha [5] presented the notation of the regular fuzzy graph. Many other researchers, such as Samanta and Pal [6], Rashmanlou and Pal [7], Rashmanlou et al [8,9], Paramik [10], Nandhini [11], Ghorai and Pal [12], Dey et. al [13], and Borzooei [14] presented much work in the domain of the fuzzy graph and its several applications in real life.…”

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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A study on vague graphs

Cited by 20 publications

References 16 publications

Novel Concepts of Domination in Vague Graphs with Application in Medicine

Novel Concepts of Domination in Vague Graphs with Application in Medicine

Study on neutrosophic graph with application in wireless network

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

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