REGULAR GRAPHS ASSOCIATED WITH RINGS

Let R be a ring with nonzero identity. By the Vonneumann regular graph of R, we mean the graph with vertices R such that there is an edge between vertices x, y if and only if x − y is a vonneumann regular element of R, denoted by G vnr− (R). In this article, the basic properties of G vnr− (R) are investigated and some characterization results regarding connectedness, diameter, girth and planarity of G vnr− (R) are given.