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Let P be a commutator poset with Z(P) its set of zero-divisors. The annihilator graph of P, denoted by AG(P), is the (undirected) graph with all elements of $Z(P){\setminus}\{0\}$ as vertices, and distinct vertices x, y are adjacent if and only if $ann(xy)\;{\neq}\;(x)\;{\cup}\;ann(y)$. In this paper, we study basic properties of AG(P).
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참고문헌 (15)
참고문헌 신청
S. Akbari / 2003 / When a zero-divisor graph is planar or a complete r-partite graph / J. Algebra 42(1):169~180
S. Akbari / 2004 / On the zero-divisor graph of a commutative ring / J. Algebra 23(2):847~855
S. Akbari / 2007 / On zero-divisor graphs of finite rings / J. Algebra 33(1):168~184
M. Alizadeh / 2012 / On the diameter and girth of zero-divisor graphs of posets / Discrete Applied Mathematics 25(3):1319~1324
D. F. Anderson / 1999 / The zero-divisor graph of a commutative ring / J. Algebra 45(2):434~447
S. Akbari / 2004 / On the zero-divisor graph of a commutative ring / J. Algebra 23(2):847~855
S. Akbari / 2007 / On zero-divisor graphs of finite rings / J. Algebra 33(1):168~184
M. Alizadeh / 2012 / On the diameter and girth of zero-divisor graphs of posets / Discrete Applied Mathematics 25(3):1319~1324
D. F. Anderson / 1999 / The zero-divisor graph of a commutative ring / J. Algebra 45(2):434~447
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