On M-Neighbourly Irregular Fuzzy Graphs

Maheswari, N.; Sekar, C.

doi:10.26708/ijmsc.2015.2.5.17

Cited by 8 publications

(9 citation statements)

References 1 publication

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“…ftbpFU5.8297in0.9279in0ptCounter example14Figure (14) Example 3. 13 Consider G = (σ, µ) be a fuzzy graph such that G = (V, E) is a path on four vertices.…”

Section: Remark 32 Letmentioning

confidence: 99%

Fuzzy Graphs

Mutab

2019

JAM

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In this paper, neighbourly irregular fuzzy graphs, neighbourly total irregular fuzzy graphs, highly irregular fuzzy graphs and highly total irregular fuzzy graphs are introduced. A necessary and suﬃcient condition under which neighbourly irregular and highly irregular fuzzy graphs are equivalent is provided. We deﬁne d2 degree of a vertex in fuzzy graphs and total d2 -degree of a vertex in fuzzy graphs and (2, k)-regular fuzzy graphs, totally (2, k)- regular fuzzy graphs are introduced. (2, k)- regular fuzzy graphs and totally (2, k)-regular fuzzy graphs are compared through various examples.

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“…ftbpFU5.8297in0.9279in0ptCounter example14Figure (14) Example 3. 13 Consider G = (σ, µ) be a fuzzy graph such that G = (V, E) is a path on four vertices.…”

Section: Remark 32 Letmentioning

confidence: 99%

Fuzzy Graphs

Mutab

2019

JAM

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“…Gani and Lathi [36] proposed the concept of irregularity, total irregularity, and total degree in a fuzzy graph. 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.…”

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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“…These concepts of regularity for both vertices and edges in fuzzy graphs led to many advancements in the structural theory of fuzzy graphs. Several relevant marquee results stemming from this research include [1, 3,4,6,[8][9][10][11][12][13][14][15][16][17][19][20][21][22][23][25][26][27][28][29][30]. The purpose of this paper is to prepare for a study of those intuitionistic fuzzy graphs that concurrently exhibit both intuitionistic fuzzy vertex and edge-regular properties.…”

Section: Introductionmentioning

confidence: 99%

“…The intention of this body of work is to serve as the necessary preliminaries for the introduction and study of those intuitionistic fuzzy graphs which are both exhibiting concurrently constant function and including those intuitionistic fuzzy graphs which are both perfectly regular and perfectly edgeregular. For an introduction to fuzzy graph theory and its basic definition, the reader is referred to [8]. For analysis notations and relevant limit theorems, the reader is referred to [24].…”

Section: Introductionmentioning

confidence: 99%

Perfectly Regular and Perfectly Edge-Regular Intuitionistic Fuzzy Graphs

2019

IJEAT

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A Perfectly regular intuitionistic fuzzy graph is an intuitionistic fuzzy graph that is both regular and totally regular. In this paper we introduce and classify these types of intuitionistic fuzzy graphs and study several of their properties, including how two classes of intuitionistic fuzzy graphs structurally relate to one another and several of their spectral properties such as isospectral intuitionistic fuzzy graphs and when the energy of intuitionistic fuzzy graph is proportional to the energy of their underlying crisp graphs. These properties are studied in particular due to having at least one constant function and .

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On M-Neighbourly Irregular Fuzzy Graphs

Cited by 8 publications

References 1 publication

Fuzzy Graphs

Fuzzy Graphs

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

Perfectly Regular and Perfectly Edge-Regular Intuitionistic Fuzzy Graphs

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