Complementary Nil G-Eccentric Domination in Fuzzy Graphs

Ismayil, A. Mohamed; Muthupandiyan, S.

doi:10.37418/amsj.9.4.28

Cited by 6 publications

(13 citation statements)

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“…A few researchers studied other domination variations which are based on above definitions, e.g. connected domination [15], total domination [17], Independent domination [24], Complementary nil domination [8], Efficient domination [32]. So we only compare our new definition with the fundamental dominations.…”

Section: Introductionmentioning

confidence: 99%

Nikfar Domination in Fuzzy Graphs

Garrett

2019

Preprint

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We introduce a new variation on the domination theme which we call nikfar domination as reducing waste of time in transportation planning. We determine the nikfar domination number  v for several classes of fuzzy graphs. The bounds is obtained for it. We prove both of the Vizing's conjecture and the Grarier-Khelladi's conjecture are monotone decreasing fuzzy graph property for nikfar domination. We obtain Nordhaus-Gaddum (NG) type results for these parameters. Finally, we discuss about nikfar dominating set of a fuzzy tree by using the bridges and -strong edges equivalence.

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Section: Introductionmentioning

confidence: 99%

Nikfar Domination in Fuzzy Graphs

Garrett

2019

Preprint

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“…[31]), see also Refs. [23,14,22,13,30,15,17,24,8,32] for further generalizations. One the contrary and quite surprisingly, there are nowhere these definitions Solving the problem of reducing waste of time in transport planning and also (separately) all others real-world problems see 4.…”

Section: Introduction and Overviewmentioning

confidence: 99%

“…The purpose of this expository article is to provide an overview of the authors' recent series of work (Refs. [31,23,14,22,13,30,15,17,24,8,32]), in which a positive answer to the problem of reducing waste of time in transport planning for the our new definition is given.…”

Section: Introduction and Overviewmentioning

confidence: 99%

Nikfar Domination in Fuzzy Graphs

M¹

2019

Preprint

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The aim of this expository article is to present recent developments in the centuries-old discussion on the interrelations between several types of domination in graphs. However, the novelty even more prominent in the newly discovered simplified presentations of several older results. The main part of this article, concerning a new domination and older one, is presented in a narrative that answers two classical questions: (i) To what extend must closing set be dominating? (ii) How strong is the assumption of domination of a closing set? In a addition, we give an overview of the results concerning domination. The problem asks how small can a subset of vertices be and contain no edges or, more generally how can small a subset of vertices be and contain other ones. Our work was as elegant as it was unexpected being a departure from the tried and true methods of this theory that had dominated the field for one fifth a century. This expository article covers all previous definitions. The inability of previous definitions in solving even one case of real-world problems due to the lack of simultaneous attentions to the worthy both of vertices and edges causing us to make the new one. The concept of domination in a variety of graphs models such as crisp, weighted and fuzzy, has been in a spotlight. We turn our attention to sets of vertices in a fuzzy graph that are so close to all vertices, in a variety of ways, and study minimum such sets and their cardinality. A natural way to introduce and motivate our subject is to view it as a real-world problem. In its most elementary form, we consider the problem of reducing waste of time in transport planning. Our goal here is to first describe the previous definitions and the results, and then to provide an overview of the flows ideas in their articles. The final outcome of this article is twofold: (i) Solving the problem of reducing waste of time in transport planning at static state; (ii) Solving and having a gentle discussions on problem of reducing waste of time in transport planning at dynamic state. Finally, we discuss the results concerning holding domination that are independent of fuzzy graphs. We close with a list of currently open problems related to this subject. Most of our exposition assumes only familiarity with basic linear algebra, polynomials, fuzzy graph theory and graph theory.

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“…[30]), Complementary nil domination (Ref. [13]), Efficient domination (Ref. [38]), strong (weak) domination (Ref.…”

Section: Introductionmentioning

confidence: 99%

Vertex Domination in Fuzzy Graphs

M¹

2019

Preprint

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We introduce a new variation on the domination theme which we call vertex domination as reducing waste of time in transportation planning and optimization of transport routes. We determine the vertex domination number $\gamma_v$ for several classes of fuzzy graphs. The bounds is obtained for it. In fuzzy graphs, monotone decreasing property and monotone increasing property are introduced. We prove both of the vizing's conjecture and the Grarier-Khelladi's conjecture are monotone decreasing fuzzy graph property for vertex domination. We obtain Nordhaus-Gaddum (NG) type results for these parameters. The relationship between several classes of operations on fuzzy graphs with the vertex domination number of them is studied. Finally, we discuss about vertex dominating set of a fuzzy tree by using the bridges and $\alpha$-strong edges equivalence.

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Complementary Nil G-Eccentric Domination in Fuzzy Graphs

Cited by 6 publications

References 0 publications

Nikfar Domination in Fuzzy Graphs

Nikfar Domination in Fuzzy Graphs

Nikfar Domination in Fuzzy Graphs

Vertex Domination in Fuzzy Graphs

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