Abstract
Let \(\Lambda \) be a numerical semigroup and \(I\subset \Lambda \) be an ideal of \(\Lambda \). The graph \(G_I(\Lambda )\) assigned to an ideal I of \(\Lambda \) is a graph with elements of \((\Lambda {\setminus } I)^*\) as vertices and any two vertices x, y are adjacent if and only if \(x+y \in I\). In this paper we give a complete characterization (up to isomorphism ) of the graph \(G_I(\Lambda )\) to be planar, where I is an irreducible ideal of \(\Lambda \). This will finally characterize non-planar graphs \(G_I(\Lambda )\) corresponding to irreducible ideal I.
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Binyamin, M.A., Ali, W., Aslam, A. et al. A Complete Classification of Planar Graphs Associated with the Ideal of the Numerical Semigroup. Iran J Sci Technol Trans Sci 46, 491–498 (2022). https://doi.org/10.1007/s40995-022-01262-0
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DOI: https://doi.org/10.1007/s40995-022-01262-0