Abstract
Let R be a commutative ring with identity. The comaximal ideal graphG(R) of R is a simple graph with its vertices are the proper ideals of R which are not contained in the Jacobson radical of R, and two vertices I1 and I2 are adjacent if and only if I1+I2=R. In this paper, a dominating set of G(R) is constructed using elements of the center when R is a commutative Artinian ring. Also we prove that the domination number of G(R) is equal to the number of factors in the Artinian decomposition of R. Also, we characterize all commutative Artinian rings(non local rings) with identity for which G(R) is planar.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: AKCE International Journal of Graphs and Combinatorics
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
