Khudhair, Hanady F. and Abdlhusein, Mohammed A. (2026) Computational Simulation of Equitable Topological Graphs. CENTRAL ASIAN JOURNAL OF MATHEMATICAL THEORY AND COMPUTER SCIENCES, 7 (3). ISSN 2660-5309

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Abstract

This study presents a computational simulation of the equitable topological graph G_q, which is constructed from a finite non-empty set endowed with the discrete topology. The vertices of the graph correspond to all non-empty proper subsets of the underlying set, while adjacency is defined according to a complementary-cardinality rule. The main objective of this work is to provide computational verification of the theoretical properties previously established for this class of graphs. An exact python-based algorithm was developed to generate the graph and compute its principal parameters, including the order, size, degree distribution, number of connected components, clique number, radius, and diameter. In addition, growth behavior was analyzed for increasing values of n, and monte carlo sampling techniques were employed to estimate graph size in cases where exact construction becomes computationally expensive. The computational results show complete agreement with the theoretical formulas and structural decomposition of the equitable topological graph. The study confirms that vertex degrees depend solely on subset cardinality and that the graph is connected only for small values of n, becoming disconnected for larger  values. Furthermore, the simulations verify the decomposition of G_q into complete bipartite components and, in the even case, an additional complete graph corresponding to the middle cardinality class. Monte carlo experiments produced highly accurate estimates with very small relative errors, demonstrating the effectiveness of sampling methods for large-scale instances. The findings highlight the usefulness of computational techniques in validating theoretical results and investigating the structural properties of topological graphs when direct analytical or manual construction becomes impractical.

Item Type:	Article
Uncontrolled Keywords:	Equitable Topological Graph, Topological Graphs, Computational Simulation, Graph Theory, Python, Monte Carlo Methods
Subjects:	H Social Sciences
Depositing User:	admin eprints
Date Deposited:	18 Jul 2026 15:00
Last Modified:	18 Jul 2026 15:00
URI:	http://eprints.umsida.ac.id/id/eprint/16782

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