The radius of unit graphs of rings

AIMS Mathematics

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