Some results on the maximal graph of commutative rings

M. Soleimani, F. Mahmudi and M. H. Naderi

Let (Γ(R))c be the maximal graph of a commutative ring with identity R whose vertices are elements of R. Two distinct vertices a and b are adjacent if and only if Ra+Rb ≠ R or there exists a maximal ideal of R containing both them. In this paper, we study some properties of two (induced) subgraphs (Γ2(R))c and (G(R))c of (Γ(R))c. 

Advanced Studies: Euro-Tbilisi Mathematical Journal, Vol. 16,  supplement issue 1 (2023), pp. 21-26