JP Journal of Algebra, Number Theory and Applications
Volume 39, Issue 2, Pages 205 - 219
(April 2017) http://dx.doi.org/10.17654/NT039020205 |
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Vnr-GRAPHS ASSOCIATED WITH RINGS
Ali Jafari Taloukolaei and Shervin Sahebi
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Abstract: Let Rbe a finite commutative ring with nonzero identity. The Vnr-graph of R, denoted by has its set of vertices equal to the set of all elements of R; distinct vertices xand yare adjacent if and only if xyis a Von Neumann regular element of R. In this article, the basic properties of are investigated and some characterization results regarding connectedness, diameter, girth and planarity of are given. |
Keywords and phrases: connectedness, diameter, girth, planarity, Vnr-graph, Von Neumann regular ring. |
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