2022/08/17 by Shahriyari, R., Nikandish, R., Tehranian, A. +1
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2208.08095
Let R be a commutative ring with identity. The co-maximal ideal graph of R, denoted by Γ(R), is a simple graph whose vertices are proper ideals of R which are not contained in the Jacobson radical of R and two distinct vertices I, J are adjacent if and only if I+J=R. In this paper, we use Gallai^,s Theorem and the concept of strong resolving graph to compute the strong metric dimension for co-maximal ideal graphs of commutative rings. Explicit formulae for the strong metric dimension, depending on whether the ring is reduced or not, are established.