Bondage and Non-Bondage Number of a Fuzzy Graph

Gani, A. Nagoor; Devi, Kavita; Akram, M.

doi:10.12732/ijpam.v103i2.7

Cited by 6 publications

(5 citation statements)

References 10 publications

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“…The basic concepts of FGs are referred from Refs. [11,14,15,18,[26][27][28][29][30][31][32][33][34][35][36][37]. An…”

Section: Contribution and Noveltymentioning

confidence: 99%

Strong Domination Index in Fuzzy Graphs

Nair,

Sunitha

2024

Fuzzy. Info. Tech.

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In this article, a novel idea of domination degree and index are defined in a fuzzy graph (FG) using weight of strong edges. The strong domination degree (SDD) of a vertex u is defined using the weight of minimal strong dominating set (MSDS) containing u. Methods to obtain an MSDS containing a particular vertex are discussed in the article. Idea of upper strong domination number, strong irredundance number, strong upper irredundance number, strong independent domination number, and strong independence number are explained and illustrated subsequently. Strong domination index (SDI) of an FG is defined using the SDD of each vertex. The concept is applied on various FGs like complete FG, complete bipartite and r-partite FG, fuzzy tree, fuzzy cycle, and fuzzy stars. Bounds involving the SDD and SDI are also obtained. Applications for SDD of a vertex is also provided.

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“…The basic concepts of FGs are referred from Refs. [11,14,15,18,[26][27][28][29][30][31][32][33][34][35][36][37]. An…”

Section: Contribution and Noveltymentioning

confidence: 99%

Strong Domination Index in Fuzzy Graphs

Nair,

Sunitha

2024

Fuzzy. Info. Tech.

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“…Definition3.3.1 [7]: Suppose 𝒢 = (𝒱, 𝜚, 𝜑) is a fuzzy graph. Any two varices in fuzzy graph are said to be fuzzy independent if there is no strong edge between them.…”

Section: Independent Set Of Chain Fuzzy Graphsmentioning

confidence: 99%

Independent Dominating Set on Chain of Fuzzy Graphs

Russel H. Majeed,

Nabeel E. Arif

2023

Tikrit J. Pure Sci.

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“…In 1988, the concept of domination, total domination, domination number, total domination number, and their bounds was discussed in various kinds of fuzzy graphs by Somasundram, and Somasundram [15] using effective edges and in 2006 by Nagoor Gani and Chandrasekaran [16] using strong edges. In 2015, Nagoor Gani et al [18] discussed bondage numbers and non-bondage numbers of fuzzy graphs. In intuitionistic fuzzy graphs, Parvathi R, Thamizhendhi G [11] studied domination.…”

Section: Literature Reviewmentioning

confidence: 99%

Application of Picture Fuzzy Bondage Set to Find Least Crowded Passenger-Friendly Railway Division in India

Banerjee

Amanathulla

2022

Preprint

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Picture fuzzy graph is a relevant mathematical tool for describing our uncertain daily life events due to unpredictable and ambiguous information. In this paper, the idea regarding picture fuzzy bondage and non-bondage sets has been introduced. Some operations on picture fuzzy bondage and non-bondage sets, like union, intersection, complement, join, and direct sum, have been described. Also, we present some theorems regarding these operations. This study presents the notion of picture fuzzy bondage number, picture fuzzy non-bondage number, and their properties. We have proposed an algorithm to determine the picture's fuzzy bondage number. Finally, an application in the communication network has been proposed for finding less crowded passengers-friendly railway divisions on Indian Railway.

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Bondage and Non-Bondage Number of a Fuzzy Graph

Cited by 6 publications

References 10 publications

Strong Domination Index in Fuzzy Graphs

Strong Domination Index in Fuzzy Graphs

Independent Dominating Set on Chain of Fuzzy Graphs

Application of Picture Fuzzy Bondage Set to Find Least Crowded Passenger-Friendly Railway Division in India

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