Some New Concepts of Fuzzy Soft Graphs

Al-Masarwah, Anas; Qamar, Majdoleen Abu

doi:10.1016/j.fiae.2017.01.003

Cited by 17 publications

(9 citation statements)

References 5 publications

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“…A study of the fuzzy graph theory has started in the pioneering paper of Rosenfeld in 1975 [1]. Following that, the concept of fuzzy graph theory was extensively studied by several authors, particularly Mordeson and Nair [2,3], Bhutani et al [4,5], Al-Masarwah and Qamar [6,7], and Akram et al [8,9].…”

Section: Introductionmentioning

confidence: 99%

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A Novel Study of Graphs Based on $m$ -Polar Cubic Structures

Muhiuddin

Alanazi

Mahboob³

et al. 2022

Journal of Function Spaces

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By combining the notions of interval-valued m-polar fuzzy graphs and m-polar fuzzy graphs, the notion of m-polar cubic graphs is first introduced. Then, the degree of a vertex in m-polar cubic graphs and complete m-polar cubic graphs is defined. After that, the concepts of direct product and strong product of m-polar cubic graphs are given. Moreover, weak isomorphism and co-weak isomorphism are defined, and examples are given to prove that weak isomorphism and co-weak isomorphism are not an isomorphism. Finally, the notion of complement m-polar cubic graphs and weak complement m-polar cubic graphs is presented.

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Section: Introductionmentioning

confidence: 99%

“…(5) Incoherent, meaningless and/or irrelevant content included in the article (6) Peer-review manipulation…”

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confidence: 99%

A Novel Study of Graphs Based on $m$ -Polar Cubic Structures

Muhiuddin

Alanazi

Mahboob³

et al. 2022

Journal of Function Spaces

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“…First, we review some definitions which can be found in [8,[21][22][23][24][25][26][27][28][29]. By a graph, we mean a pair G * = (V, E), where V is the set and E is a relation on V. The elements of V are vertices of G * and the elements of E are edges of G * .…”

Section: Preliminariesmentioning

confidence: 99%

Total and Secure Domination for Corona Product of Two Fuzzy Soft Graphs

Karbasioun

Ameri

2021

Fuzzy Information and Engineering

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Fuzzy sets and soft sets are two different soft computing models for representing vagueness and uncertainty. On the other domination is a rapidly developing area of research in graph theory, and its various applications to ad hoc networks, distributed computing, social networks and web graphs partly explain the increased interest. This concept was introduced by [Benecke S, Cockayne EJ, Mynhardt CM. Secure total domination in graphs. Util Math. 2007;74:247-259.] in 2007 and Go and Canoy continue the study of these notions [Canoy RS, Go CE. Domination in the corona and join of graphs. Int Math Forum. 2011;6(16):763-771.] and afterward introduce total dominating and secure total dominating sets. Also graph operations like corona product play a very important role in mathematical chemistry, since some chemically interesting graphs can be obtained from some simpler graphs by different graph operations. In this paper, we characterised the dominating, total dominating, and secure total dominating sets in the corona of two fuzzy soft connected.

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“…Definition: 3. 9 The length of the fuzzy soft walk in D is L D (W) = µ where a i = ( ( ), ( )) e ∈ , ∈ Example: 3. 3 Consider the V = { …”

Section: Definition: 37mentioning

confidence: 99%