A Conjecture for the Clique Number of Graphs Associated with Symmetric Numerical Semigroups of Arbitrary Multiplicity and Embedding Dimension

Autor: Amal S. Alali, Muhammad Ahsan Binyamin, Maria Mehtab
Jazyk: angličtina
Rok vydání: 2024
Předmět:
Zdroj: Symmetry, Vol 16, Iss 7, p 854 (2024)
Druh dokumentu: article
ISSN: 2073-8994
DOI: 10.3390/sym16070854
Popis: A subset S of non-negative integers No is called a numerical semigroup if it is a submonoid of No and has a finite complement in No. An undirected graph G(S) associated with S is a graph having V(G(S))={vi:i∈No∖S} and E(G(S))={vivj⇔i+j∈S}. In this article, we propose a conjecture for the clique number of graphs associated with a symmetric family of numerical semigroups of arbitrary multiplicity and embedding dimension. Furthermore, we prove this conjecture for the case of arbitrary multiplicity and embedding dimension 7.
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