On the Planarity of Graphs Associated with Symmetric and Pseudo Symmetric Numerical Semigroups

Yongsheng Rao, Muhammad Ahsan Binyamin (), Adnan Aslam, Maria Mehtab and Shazia Fazal
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Yongsheng Rao: Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China
Muhammad Ahsan Binyamin: Department of Mathematics, GC University, Faisalabad 38000, Pakistan
Adnan Aslam: Department of Natural Sciences and Humanities, University of Engineering and Technology, Lahore 54000, Pakistan
Maria Mehtab: Department of Mathematics, GC University, Faisalabad 38000, Pakistan
Shazia Fazal: Department of Mathematics, GC University, Faisalabad 38000, Pakistan

Mathematics, 2023, vol. 11, issue 7, 1-11

Abstract: Let S ( m , e ) be a class of numerical semigroups with multiplicity m and embedding dimension e . We call a graph G S an S ( m , e ) -graph if there exists a numerical semigroup S ∈ S ( m , e ) with V ( G S ) = { x : x ∈ g ( S ) } and E ( G S ) = { x y ⇔ x + y ∈ S } , where g ( S ) denotes the gap set of S . The aim of this article is to discuss the planarity of S ( m , e ) -graphs for some cases where S is an irreducible numerical semigroup.

Keywords: numerical semigroup; Frobenius number; genus; clique number; planarity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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