The rings considered in this article are commutative with identity. This article is motivated by the work on comaximal graphs of rings. In this article, with any ring $R$, we associate an undirected graph denoted by $G(R)$, whose vertex set is the set of all elements of $R$ and distinct vertices $x,y$ are joined by an edge in $G(R)$ if and only if $Rx\cap Ry = Rxy$. In Section 2 of this article, we classify rings $R$ such that $G(R)$ is complete and we also consider the problem of determining rings $R$ such that $\chi(G(R)) = \omega(G(R))< \infty$. In Section 3 of this article, we classify rings $R$ such that $G(R)$ is planar.
Visweswaran, S., & Parejiya, J. (2017). A Note on a graph associated to a commutative ring. Journal of Algebra and Related Topics, 5(1), 61-82. doi: 10.22124/jart.2017.2399
MLA
S. Visweswaran; J. Parejiya. "A Note on a graph associated to a commutative ring". Journal of Algebra and Related Topics, 5, 1, 2017, 61-82. doi: 10.22124/jart.2017.2399
HARVARD
Visweswaran, S., Parejiya, J. (2017). 'A Note on a graph associated to a commutative ring', Journal of Algebra and Related Topics, 5(1), pp. 61-82. doi: 10.22124/jart.2017.2399
VANCOUVER
Visweswaran, S., Parejiya, J. A Note on a graph associated to a commutative ring. Journal of Algebra and Related Topics, 2017; 5(1): 61-82. doi: 10.22124/jart.2017.2399
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