Some graph theoretical properties over zero-divisor graphs of special finite commutative rings
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Let R be a commutative ring with identity and let Z(R) be the set of zero-divisors of R. It has been widely studied the notion of the zero-divisor graph of R which is de ned by Γ(R) = Z(R) / {0} such that the distinct vertices x and y are adjacent if and only if xy = 0. As main results of this paper, by considering R = Z_p x Z_q for di¤erent primes p and q, we prove some graph theoretical properties over Γ(Z_p x Z_q) which are the generalizations of the results in [12].
Abstract
Let R be a commutative ring with identity and let Z(R) be the set of zero-divisors of R. It has been widely studied the notion of the zero-divisor graph of R which is de ned by Γ(R) = Z(R) / {0} such that the distinct vertices x and y are adjacent if and only if xy = 0. As main results of this paper, by considering R = Z_p x Z_q for di¤erent primes p and q, we prove some graph theoretical properties over Γ(Z_p x Z_q) which are the generalizations of the results in [12].
참고문헌 (13)
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