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Optimization of disaster management using split domination in picture fuzzy graphs

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Abstract

Fuzzy graphs, including their extensions such as intuitionistic fuzzy graphs and picture fuzzy graphs, find substantial applications in diverse natural and human-made systems. The exploration of various domination types in picture fuzzy graphs has become key topics in this field due to their extensive practical use. This paper describes the idea of split, non-split domination, minimum, maximum and supremum split dominating sets and minimum, maximum and supremum split domination numbers in the picture fuzzy environment. Some properties and theorems regarding split, non-split domination in picture fuzzy graphs have been presented. Classifications of strong edges are introduced and various types of domination are presented in picture fuzzy graphs. Algorithms to find the minimum split dominating set and the set of strong edges using the membership matrix of the picture fuzzy graph have been presented in this paper. A real life application regarding disaster management using split domination in picture fuzzy graphs has also been presented, which helps to manage disaster in a better way.

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No data were used to support this study.

Abbreviations

PFG:

Picture fuzzy graph

pfv :

Picture fuzzy vertex

pfe :

Picture fuzzy edge

pfse :

Picture fuzzy strong edge

pfd-Set:

Picture fuzzy dominating set

pfsd-Set:

Picture fuzzy split dominating set

pfnsd-Set:

Picture fuzzy non split dominating set

\(pfm_{l}sd\)-Set:

Minimal picture fuzzy split dominating set

\(pfm_{i}sd\)-Set:

Minimum picture fuzzy split dominating set

\(pfm_{x}sd\)-Set:

Maximum picture fuzzy split dominating set

\(pfs_{m}sd\)-Set:

Supremum picture fuzzy split dominating set

\(\delta _{s}(G)\) :

Picture fuzzy split domination number of G

\(\delta ^{u}_{s}(G)\) :

Picture fuzzy upper split domination number of G

\(\delta ^{s}_{s}(G)\) :

Picture fuzzy super split domination number of G

\(\delta _{ns}(G)\) :

Picture fuzzy non split domination number of G

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  1. Department of Mathematics, Sidho-Kanho-Birsha University, Purulia, 723104, India

    Avisek Banerjee

  2. Department of Mathematics, Raghunathpur College, Raghunathpur, Purulia, 723133, India

    Sk Amanathulla

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  1. Avisek Banerjee
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Banerjee, A., Amanathulla, S. Optimization of disaster management using split domination in picture fuzzy graphs. J. Appl. Math. Comput. 70, 435–459 (2024). https://doi.org/10.1007/s12190-023-01965-6

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  • DOI: https://doi.org/10.1007/s12190-023-01965-6

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