Characterization of graphs associated with the ideal of numerical semigroups (Q827204)

Summary: Let \(I\) be an ideal of a numerical semigroup \(\Lambda\). We define an undirected graph \(G_I\Lambda\) with vertex set \(\{v_i : i \in (\Lambda \backslash I)^* = (\Lambda \backslash I) - \{0\}\}\) and edge set \(\{ v_i v_j \Longleftrightarrow i + j \in I\}\). The aim of this article is to discuss the connectedness, girth, completeness, and some other related properties of the graph \(G_I (\Lambda)\).