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Volume 14
Issue 9
10.3390/axioms14090669
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

On Structural Characterization and Computation of the Diameter and Girth of Bipartite Gap Poset Graphs with Python Application

by
Maria Mehtab
1,
Muhammad Ahsan Binyamin
1,
Syed Sheraz Asghar
1,
Amal S. Alali
2,* and
Khawar Mehmood
3
1
Department of Mathematics, Government College University, Faisalabad 38000, Pakistan
2
Department of Mathematical Sciences, College of Science, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
3
Department of Mathematics, College of Science, Sultan Qaboos University, P.O. Box 36, Muscat 123, Oman
*
Author to whom correspondence should be addressed.
Axioms 2025, 14(9), 669; https://doi.org/10.3390/axioms14090669
Submission received: 25 July 2025 / Revised: 23 August 2025 / Accepted: 26 August 2025 / Published: 29 August 2025
(This article belongs to the Special Issue Graph Invariants and Their Applications)
Versions Notes

Abstract

In this article, a correspondence between some important classes of numerical semigroups and well-known families of bipartite graphs has been established. Also, it has been demonstrated that, if m(S) is the multiplicity of a numerical semigroup S, then the diameter and the girth of bipartite gap poset graphs are bounded by the numbers 2m(S)−3 and m(S)−1, respectively. Moreover, the Python code to compute the diameter and girth of gap poset graphs has been implemented.
Keywords: elementary numerical semigroup; partial order; bipartite graph; connected graph; diameter; girth elementary numerical semigroup; partial order; bipartite graph; connected graph; diameter; girth

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MDPI and ACS Style

Mehtab, M.; Binyamin, M.A.; Asghar, S.S.; Alali, A.S.; Mehmood, K. On Structural Characterization and Computation of the Diameter and Girth of Bipartite Gap Poset Graphs with Python Application. Axioms 2025, 14, 669. https://doi.org/10.3390/axioms14090669

AMA Style

Mehtab M, Binyamin MA, Asghar SS, Alali AS, Mehmood K. On Structural Characterization and Computation of the Diameter and Girth of Bipartite Gap Poset Graphs with Python Application. Axioms. 2025; 14(9):669. https://doi.org/10.3390/axioms14090669

Chicago/Turabian Style

Mehtab, Maria, Muhammad Ahsan Binyamin, Syed Sheraz Asghar, Amal S. Alali, and Khawar Mehmood. 2025. "On Structural Characterization and Computation of the Diameter and Girth of Bipartite Gap Poset Graphs with Python Application" Axioms 14, no. 9: 669. https://doi.org/10.3390/axioms14090669

APA Style

Mehtab, M., Binyamin, M. A., Asghar, S. S., Alali, A. S., & Mehmood, K. (2025). On Structural Characterization and Computation of the Diameter and Girth of Bipartite Gap Poset Graphs with Python Application. Axioms, 14(9), 669. https://doi.org/10.3390/axioms14090669

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