Recently, an interest is developed in estimating genus of the zero-divisor graph of a ring. In this note we investigate genera of graphs of a class of zero-divisor rings (a ring in which every element is a zero divisor). We call a ring R to be right absorbing if for a; b in R, ab is not 0, then ab D a. We first show that right absorbing rings are generalized right Klein 4-rings of characteristic two and that these are non-commutative zero-divisor local rings. The zero-divisor graph of such a ring is proved to be precisely the union of a complete graph and a complete bipartite graph. Finally, we have estimated lower and upper bounds of the genus of such a ring.
@article{bwmeta1.element.doi-10_1515_math-2015-0050,
author = {Syed Khalid Nauman and Basmah H. Shafee},
title = {A class of zero divisor rings in which every graph is precisely the union of a complete graph and a complete bipartite graph},
journal = {Open Mathematics},
volume = {13},
year = {2015},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2015-0050}
}
Syed Khalid Nauman; Basmah H. Shafee. A class of zero divisor rings in which every graph is precisely the union of a complete graph and a complete bipartite graph. Open Mathematics, Tome 13 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2015-0050/
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