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

A subset S of non-negative integers N o is called a numerical semigroup if it is a submonoid of N o and has a finite complement in N o . An undirected graph G (S) associated with S is a graph having V (G (S)) = { v i : i ∈ N o ∖ S } and E (G (S)) = { v i v j ⇔ 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. [ABSTRACT FROM AUTHOR]