Zero-divisor graphs of amalgamations - Kabbaj, Salah-Eddine; Mimouni, Abdeslam (MATHEMATICA SCANDINAVICA, 2018)
Let fA→ B be a homomorphism of commutative rings and let J be an ideal of B. The amalgamation of A with B along J with respect to f is the subring of A× B given by \[ A^fJ:={(a,f(a)+j) aA, jJ}. \] This paper investigates the zero-divisor graph of amalgamations. Our aim is to characterize when the graph is complete and compute its diameter and girth for various contexts of amalgamations. The new results recover well-known results on duplications, and yield new and original examples issued from amalgamations.