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Article | Open Access

Strong Domination Index in Fuzzy Graphs

Kavya R. Nair1( ), Muraleedharan Shetty Sunitha1
Department of Mathematics, National Institute of Technology, Calicut 673601, India
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Abstract

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.

Keywords

strong domination degreestrong domination regular fuzzy graph (FG)strong domination indexupper strong domination numberstrong irredundance numberstrong upper irredundance numberstrong independent domination numberstrong independence numberr-partite FG

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Fuzzy Information and Engineering
Volume 16 Issue 1,
March 2024
Pages 1-23
DOI: 10.26599/FIE.2023.9270028
Cite this article:
Nair KR, Sunitha MS. Strong Domination Index in Fuzzy Graphs. Fuzzy Information and Engineering, 2024, 16(1): 1-23. https://doi.org/10.26599/FIE.2023.9270028

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Received: 25 September 2023
Revised: 10 November 2023
Accepted: 10 December 2023
Published: 30 March 2024
© The Author(s) 2024. Published by Tsinghua University Press.

This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
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