TY - JOUR
ID - 15047
TI - Some results on the comaximal ideal graph of a commutative ring
JO - Transactions on Combinatorics
JA - TOC
LA - en
SN - 2251-8657
AU - Dorbidi, Hamid Reza
AU - Manaviyat, Raoufeh
AD - University of Jiroft,Jiroft, Kerman, Iran
AD - Payame Noor University, Tehran, Iran
Y1 - 2016
PY - 2016
VL - 5
IS - 4
SP - 9
EP - 20
KW - Comaximal ideal graph
KW - Genus of graph
KW - Domination Number
KW - Independence number
DO - 10.22108/toc.2016.15047
N2 - Let $R$ be a commutative ring with unity. The comaximal ideal graph of $R$, denoted by $\mathcal{C}(R)$, is a graph whose vertices are the proper ideals of $R$ which are not contained in the Jacobson radical of $R$, and two vertices $I_1$ and $I_2$ are adjacent if and only if $I_1 +I_2 = R$. In this paper, we classify all comaximal ideal graphs with finite independence number and present a formula to calculate this number. Also, the domination number of $\mathcal{C}(R)$ for a ring $R$ is determined. In the last section, we introduce all planar and toroidal comaximal ideal graphs. Moreover, the commutative rings with isomorphic comaximal ideal graphs are characterized. In particular we show that every finite comaximal ideal graph is isomorphic to some $\mathcal{C}(\mathbb{Z}_n)$.
UR - https://toc.ui.ac.ir/article_15047.html
L1 - https://toc.ui.ac.ir/article_15047_e2760f540dc55e62152260c257848270.pdf
ER -