Intuitionistic Fuzzy Hypergraph Laplacians and Dominating Transversals for Resilient Discrete Network Design

Year : 2026 | Volume : 13 | Issue : 02 | Page : 15 21
By

Markala Karthik,

S. Vairachilai,

Mohammed Almakki,

Mohammed El Khider,

  1. Assistant Professor, 1Department of Electrical and Electronics Engineering, SR University, Warangal, Telangana, India
  2. Associate Professor, School of Computer Science and Artificial Intelligence, SR University, Warangal, Telangana, India
  3. Assistant Professor, School of Engineering, Architecture and Interior Design, Amity University Dubai, Dubai, United Arab Emirates
  4. Assistant Professor, Department of General Undergraduate Curriculum Requirements, University of Dubai, Dubai, United Arab Emirates

Abstract

This manuscript develops a discrete mathematical framework for resilience analysis on networks whose interactions are polyadic, uncertain, and partially conflicting. Classical graphs compress multi-way coordination into pairwise edges, while ordinary fuzzy graphs often ignore the non-membership information that becomes critical in emergency logistics, infrastructure interdependence, and cyberphysical coordination. We therefore formulate an intuitionistic fuzzy hypergraph in which each vertex hyperedge incidence carries membership, non-membership, and hesitation, and we construct a hesitation-aware Laplacian that remains symmetric and positive semidefinite. On this basis, two coupled optimization objects are introduced: an uncertainty-regularized algebraic connectivity that quantifies structural robustness, and a dominating transversal number that quantifies the minimum control set needed to supervise all higher-order interactions. We derive lower and upper bounds linking the second Laplacian eigenvalue, weighted vertex degrees, and domination cost; establish a perturbation estimate showing how hesitation inflation degrades connectivity; and propose a greedy spectral-transversal algorithm with near-linear practical complexity in sparse hypergraphs. A synthetic benchmark on modular response networks shows that the proposed operator separates fragile and resilient designs more sharply than pairwise surrogates and identifies low-cardinality control sets with lower uncertainty burden. The paper is aligned with discrete structures, logic-oriented uncertainty, set-theoretic modeling, relations, functions, and matrix-based analysis, while also incorporating recent intuitionistic fuzzy, hypergraph, and fuzzy optimization literature. The resulting framework is intended as a submission-ready theoretical and computational study for a journal audience in discrete mathematical structures.

Keywords: intuitionistic fuzzy hypergraph, discrete Laplacian, dominating transversal, spectral resilience, higher-order network, fuzzy optimization

[This article belongs to Research & Reviews: Discrete Mathematical Structures ]

How to cite this article: Markala Karthik, S. Vairachilai, Mohammed Almakki, Mohammed El Khider. Intuitionistic Fuzzy Hypergraph Laplacians and Dominating Transversals for Resilient Discrete Network Design. Research & Reviews: Discrete Mathematical Structures. 2026; 13(02):15-21.
How to cite this URL: Markala Karthik, S. Vairachilai, Mohammed Almakki, Mohammed El Khider. Intuitionistic Fuzzy Hypergraph Laplacians and Dominating Transversals for Resilient Discrete Network Design. Research & Reviews: Discrete Mathematical Structures. 2026; 13(02):15-21. Available from: https://journals.stmjournals.com/rrdms/article=2026/view=250988

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Regular Issue Subscription Original Research
Volume 13
Issue 02
Received 13/04/2026
Accepted 19/05/2026
Published 30/05/2026
Publication Time 47 Days

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