Innovations in Soft Graph Theory: Advanced Models, Hybrid Structures, and Emerging Applications

D.Thenge-Mashale, Jyoti

doi:https://doi.org/10.55041/ijsmt.v2i4.468

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INNOVATIONS IN SOFT GRAPH THEORY: ADVANCED MODELS, HYBRID STRUCTURES, AND EMERGING APPLICATIONS

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Jyoti D.Thenge-Mashale

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DOI: 10.55041/ijsmt.v2i4.468

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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Abstract

Soft graph theory has emerged as a robust mathematical framework for modeling uncertainty through parameterized structures. In recent years, significant advancements have been made by integrating soft sets with neutrosophic, fuzzy, and rough frameworks. This paper presents a comprehensive study of modern innovations in soft graph theory, including neutrosophic soft graphs, soft rough hybrid graphs, and multi-layer parameterized models. A novel structure, the Parameterized Multi-Layer Soft Graph (PMLSG), is proposed to address limitations in existing models. Theoretical properties, algebraic operations, and application perspectives are discussed. A detailed and plagiarism-safe literature review highlights research gaps and motivates future directions in uncertain graph modeling.

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This article has undergone plagiarism screening and double-blind peer review. Editorial policies have been followed. Authors retain copyright under CC BY-NC 4.0 license. The research complies with ethical standards and institutional guidelines.

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