In this paper,we introduce a new graph whose vertices are the non-zero zerodivisors of a commutativc ring R、and for distincts elements x and y in the set Z(R)^(*)of the non-zero zero-divisors of R,x and y are adjacen...In this paper,we introduce a new graph whose vertices are the non-zero zerodivisors of a commutativc ring R、and for distincts elements x and y in the set Z(R)^(*)of the non-zero zero-divisors of R,x and y are adjacent if and only if xy=0 or x+y∈Z(R).We present some properties and examples of this graph,and we study its relationship with the zero-divisor graph and with a subgraph of the total graph of a commutative ring.展开更多
文摘In this paper,we introduce a new graph whose vertices are the non-zero zerodivisors of a commutativc ring R、and for distincts elements x and y in the set Z(R)^(*)of the non-zero zero-divisors of R,x and y are adjacent if and only if xy=0 or x+y∈Z(R).We present some properties and examples of this graph,and we study its relationship with the zero-divisor graph and with a subgraph of the total graph of a commutative ring.
