期刊论文详细信息
AIMS Mathematics | |
The radius of unit graphs of rings | |
Zhiqun Li1  Huadong Su1  | |
[1] School of Sciences, Beibu Gulf University, Qinzhou 535011, China; | |
关键词: unit graph; radius; self-injective ring; unit sum number; ring extension; | |
DOI : 10.3934/math.2021667 | |
来源: DOAJ |
【 摘 要 】
Let R be a ring with nonzero identity. The unit graph of R is a simple graph whose vertex set is R itself and two distinct vertices are adjacent if and only if their sum is a unit of R. In this paper, we study the radius of unit graphs of rings. We prove that there exists a ring R such that the radius of unit graph can be any given positive integer. We also prove that the radius of unit graphs of self-injective rings are 1, 2, 3, ∞. We classify all self-injective rings via the radius of its unit graph. The radius of unit graphs of some ring extensions are also considered.
【 授权许可】
Unknown