TY - JOUR
ID - 2399
TI - A Note on a graph associated to a commutative ring
JO - Journal of Algebra and Related Topics
JA - JART
LA - en
SN - 2345-3931
AU - Visweswaran, S.
AU - Parejiya, J.
AD - Saurashtra University
Y1 - 2017
PY - 2017
VL - 5
IS - 1
SP - 61
EP - 82
KW - Comaximal graph of a ring
KW - complete graph
KW - chromatic number
KW - clique number
KW - planar graph
DO - 10.22124/jart.2017.2399
N2 - 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 $Rxcap Ry = Rxy$. 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.
UR - https://jart.guilan.ac.ir/article_2399.html
L1 - https://jart.guilan.ac.ir/article_2399_1591422012d4680950f3bb1760b533a6.pdf
ER -