Semipotent Rings Whose Unit Graphs Are Planar

• 作者: Huadong Su Yangjiang Wei
• 来源期刊: 代数集刊（英文版）
• 关键词: unit graph planar graph semipotent ring unit
• 年，卷（期）: 2020,（2）
• 页码范围: 311-318
• 页数: 8页
• 语种: 英文
• DOI: 10.1142/S1005386720000255

摘要

The unit graph of a ring is the simple graph whose vertices are the elements of the ring and where two distinct vertices are adjacent if and only if their sum is a unit of the ring.A simple graph is said to be planar if it can be drawn on the plane in such a way that its edges intersect only at their endpoints.In this note,we completely characterize the semipotent rings whose unit graphs are planar.As a consequence,we list all semilocal rings with planar unit graphs.