关于格的可比性图的同构定理
On Isomorphism theorem of the Comparability Graph of Lattices
AI总结：
本文研究了格的可比性图，刻画了图同构下保持的格性质，构造了非同构但可比性图同构的格，并找到了两类格使得图同构蕴含格同构。
摘要：
近年来，研究人员积极贡献于与代数结构和序结构相关的图领域。一个基本问题是，我们能否从关联图中推断出代数或序结构，反之亦然。在本文中，我们给出了可比性图及其关联格的刻画。特别地，我们确定了在图同构下保持的格的一些性质。我们还提供了一种构造非同构但可比性图同构的格的技术。此外，我们找到了两类格，其中图同构蕴含格同构。
英文摘要：
In recent years, researchers have actively contributed to the field of graphs associated with algebraic structures and ordered structures. It is a fundamental question to ask whether we infer algebraic or ordered structure from associated graphs and vice versa. In this paper, we gave characterizations about comparability graphs and associated lattices. In particular, we determined some properties of lattices that are preserved under the graph isomorphism. We have also provided a technique to construct non-isomorphic lattices with isomorphic comparability graphs. Also, we find two classes of lattices in which the graph isomorphism gives the lattice isomorphism.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
