New concepts of regular and (highly) irregular vague graphs with applications

Darabian, Elham; Borzooei, Rajab Ali; Rashmanlou, Hossein; Azadi, Mehrdad

doi:10.1016/j.fiae.2017.06.003

Cited by 6 publications

(1 citation statement)

References 8 publications

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“…Maheswari and Sekar [37] proposed the notation of the d 2 -vertex in a fuzzy graph and also described several properties on the d 2 -vertex degree of a fuzzy graph. Darabian et al [38] presented the idea of the d m -regular vague graph, td m -regular vague graph, m-highly irregular vague graph, and m-highly total irregular vague graph, and they discussed some properties of those graphs. They described some real-life applications (e.g., fullerene molecules, wireless networks, and road networks) of regular vague graphs.…”

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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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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Fundamentals of Fuzzy Graphs

Pal

Samanta²,

Ghorai

2020

Modern Trends in Fuzzy Graph Theory

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A study on regular picture fuzzy graph with applications in communication networks

Xiao

Dey²,

Sơn

2020

IFS

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Picture fuzzy graph (PFG) is an extended version of intuitionistic fuzzy graph (IFG) to model the uncertain real world problems, in which IFG may fail to model those problems properly. PFG is more precise, flexible and compatible than IFG to deal the real-life scenarios which consists of information these types: yes, abstain, no and refusal. The main focus of our study is to present the concept of isomorphic PFG, regular PFG (RPFG) and picture fuzzy multigraph. In this paper, we present the notation of RPFG. Many different types of RPFGs such as regular strong PFG, regular complete PFG, complete bipartite PFG and regular complement PFG are introduced. We also describe the concepts of dn and tdn-degree of a vertex in a RPFG. Based on those two types of degrees, we classify the regularity of PFG into 3 type’s namely, dn- RPFG, tdn-RPFG and n- highly irregular PFG. Several theorems of those RPFG are presented here. We define the busy vertex and free vertex in a RPFG. We present the notations of μ-complement, homomorphism, isomorphism, weak isomorphism and co weak isomorphism of RPFG. Some significant theorems on isomorphism and μ- complement of RPFG are derived here. We also introduce the notation of picture fuzzy multigraph. We present a mathematical model of communication network and transportation network by using picture fuzzy multigraph and real time data are collected so that the transportation network/communication network can work efficiently.

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New concepts of regular and (highly) irregular vague graphs with applications

Cited by 6 publications

References 8 publications

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

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

Fundamentals of Fuzzy Graphs

A study on regular picture fuzzy graph with applications in communication networks

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