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 ...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.展开更多
基金supported by the National Natural Science Foundation of China(11661013,11661014,11961050)Guangxi Natural Science Foundation(2016GXNSFCA380014,2016GXNSFDA380017).
文摘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.
