Some of the graph energies of zero-divisor graphs of finite commutative rings

In this paper, we investigate some of the graph energies of the zero-divisor graph Γ(R) of finite commutative rings R. Let Z(R) be the set of zero-divisors of a commutative ring R with non-zero identity and Z∗(R) = Z(R) \ {0}. The zero-divisor graph of R, denoted by Γ(R), is a simple graph whose vertex set in Z∗(R) and two vertices u and v are adjacent if and only if uv = vu = 0. We investigate some energies of Γ(R) for the commutative rings R ≃ Zp2 × Zq, R ≃ Zp × Zp × Zp and R ≃ Zp × Zp × Zp × Zp where p, q the prime numbers.