Journal of Algebra and its Applications, ( ISI ), Volume (12), No (3), Year (2013-5) , Pages (1250179-18)

Title : ( THE JACOBSON GRAPH OF COMMUTATIVE RINGS )

Authors: Ali Azimi , Ahmad Erfanian , Mohammad Farrokhi Derakhshandeh Ghouchan ,

Access to full-text not allowed by authors

Citation: BibTeX | EndNote

Abstract

Let R be a commutative ring with nonzero identity. Then the Jacobson graph of R, denoted by JR, is defined as a graph with vertex set R\\J(R) such that two distinct vertices x and y are adjacent if and only if 1 − xy is not a unit of R. We obtain some graph theoretical properties of JR including its connectivity, planarity and perfectness and we compute some of its numerical invariants, namely diameter, girth, dominating number, independence number and vertex chromatic number and give an estimate for its edge chromatic number.

Keywords

diameter; girth; connectivity; planarity; perfectness; dominating number; independence number; clique number; vertex and edge chromatic number; local ring.