An investigation on maximal graphs associated to commutative rings

A. Sharma, B. Davvaz

Let $R$ be a commutative ring with non-zero identity. Let Γ(R) denotes the maximal graph corresponding to the non-unit elements of R, that is, Γ(R) is a graph with vertices as non-unit elements of R, where two distinct vertices a and b are adjacent if and only if there is a maximal ideal of R containing both. In this paper, we characterize rings for which L(Γ(R)) is planar. Also, we characterize the rings for which the graphs Γ(R) and L(Γ(R)) are split graphs. 

Advanced Studies: Euro-Tbilisi Mathematical Journal, Vol. 18(1) (2025), pp. 45-52