Mathematics and Computational Sciences

Applying Cech rough closure theory to binary hypercube graphs

Document Type : Original Article

Authors

Simson Jackson
Anto Snow Sherine I

Department of Mathematics, V. O. Chidambaram College, Thoothukudi-628008, Manonmaniam Sundaranar University, Abishekaptti,Tirunelveli-627012

https://doi.org/10.30511/mcs.2025.2075046.1509
Abstract
The present study examines hypercube graphs through the lens of Čech rough closure theory (ČRCT). Leveraging the binary representation and inherent symmetry of hypercubes, we introduce a closure-based approach for modelling uncertainty and vagueness in discrete spaces. Our method constructs set approximations from vertex adjacency, offering a systematic way to examine neighbourhood configurations. To illustrate the applicability of this framework, we present examples on low-dimensional hypercubes. The findings highlight how rough closure concepts can enrich graph-theoretic analysis and provide flexible tools for developing models in discrete mathematics.

Keywords

Rough closure hypercube space
Rough closure hypercube operator
Rough hypercube interior
Rough hypercube neighbourhood
Rough hypercube continuous

Subjects

[1] Alka Benny and Lakshmi Jayan, A study on interconnection networks and graphs, (2019). 
[2] Cech.E, Topological spaces, Inter science Publishers, John Wiley and Sons, New York, (1966).
[3] Cech.E, Topological spaces, Topological Papers of Eduard Cech, Academia. Praque (1968), 436-472.
[4] Pawlak, Z. (1982). Rough sets: power set hierarchy. Polish Academy of Sciences [PAS]. Institute of Computer Science. 
[5] Pawlak, Z. (1996). Rough sets, rough relations and rough functions. Fundamenta informaticae, 27(2-3), 103-108.
Mathematics and Computational Sciences
Volume 6, Issue 4
Autumn 2025
Pages 44-49

  • Receive Date 18 October 2025
  • Revise Date 22 November 2025
  • Accept Date 24 November 2025

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