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 \Gamma(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)\setminus \{۰\}. The zero-divisor graph of R, denoted by \Gamma(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=۰. We investigate some energies of \Gamma(R) for the commutative rings R\simeq \mathbb{Z}_{p^۲}\times \mathbb{Z}_{q}, R\simeq \mathbb{Z}_{p}\times \mathbb{Z}_{p}\times \mathbb{Z}_{p} and R\simeq \mathbb{Z}_{p}\times \mathbb{Z}_{p}\times \mathbb{Z}_{p}\times \mathbb{Z}_{p} where p, q the prime numbers.

کلیدواژه ها:

Commutative ring ، Zero-divisor graph ، line graph ، Minimum edge dominating energy ، Laplacian energy