부산대학교 도서관

Summary: ``Let $R$ be a commutative ring with unity. Let $N il(R)$ be the set of all nilpotent elements of $R$ and $\overline{N il(R)} = R \setminus N il(R)$ be the set of all non-nilpotent elements of $R$. The non-nilpotent graph of $R$ is a simple undirected graph $G_{NN} (R)$ with $\overline{N il(R)}$ as vertex set and any two distinct vertices $x$ and $y$ are adjacent if and only if $x + y \in N il(R)$. In this paper, we introduce and discuss the basic properties of the graph $G_{NN} (R)$. We also study the diameter and girth of $G_{NN} (R)$. Further, we determine the domination number and the bondage number of $G_{NN} (R)$. We establish a relation between diameter and domination number of $G_{NN} (R)$. We also establish a relation between girth and bondage number of $G_{NN} (R)$.''