论文标题
与数值半群的理想相关的平面图的分类
Classification of Planar Graphs Associated to the Ideal of the Numerical Semigroup
论文作者
论文摘要
令$λ$为数值半群，$ i \子集λ$为$λ$的理想。分配给理想的$ i $ of $λ$的图$ g_i（λ）$是$（λ\ setminus i）^*$的元素的图形，并且在i $中仅当$ x+y \时，任何两个dertices $ x，y $才相邻。在本文中，我们给出了图形$ g_i（λ）$的完整表征（直至同构）为平面，其中$ i $是$λ$的不可约理想。最终将表征与不可约理想$ i $相对应的非平面图$ g_i（λ）$。
Let $Λ$ be a numerical semigroup and $I\subset Λ$ be an ideal of $Λ$. The graph $G_I(Λ)$ assigned to an ideal $I$ of $Λ$ is a graph with elements of $(Λ\setminus I)^*$ 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 $G_I(Λ)$ to be planar, where $I$ is an irreducible ideal of $Λ$. This will finally characterize non planar graphs $G_I(Λ)$ corresponding to irreducible ideal $I$.
