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)