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

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 pos...

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Bibliographic Details
Published inAxioms Vol. 14; no. 9; p. 669
Main Authors Mehtab, Maria, Binyamin, Muhammad Ahsan, Asghar, Syed Sheraz, Alali, Amal S., Mehmood, Khawar
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 29.08.2025
Subjects
Algebra
bipartite graph
Coding theory
Combinatorics
Communication
Communications networks
Computer science
connected graph
diameter
elementary numerical semigroup
girth
Graph theory
Graphs
Group theory
partial order
Python
Semigroups
Software
Structural analysis
Visualization
Pakistan
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ISSN2075-1680
2075-1680
DOI10.3390/axioms14090669

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Summary: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.
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content type line 14
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms14090669