some graph parameters of the zero-divisor graphs of finite commutative rings

In this paper, some graph parameters of the zero-divisor graph γ(r) of a finite commutative ring r for r ≃ zp × zp2 and r ≃ zp × z2p where p > 2 a prime, are investigated. the graph γ(r) is a simple graph whose vertex set is the set of non-zero zero-divisors of a commutative ring r with non-zero identity and two vertices u and v are adjacent if and only if uv = vu = 0. in this paper, we study some of the topological indices such as graph energies, the zagreb indices and the domination parameters of graphs γ( zp × zp2 ) and γ (zp × z2p)