Some results on the maximal graph of commutative rings
M. Soleimani, F. Mahmudi, M. H. Naderi
Abstract
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.
Topics & Concepts
Commutative ringCombinatoricsMathematicsGraphCommutative propertyMaximal idealIdeal (ethics)Discrete mathematicsPhilosophyEpistemologyRings, Modules, and AlgebrasFinite Group Theory ResearchAdvanced Topics in Algebra