# ANNIHILATOR GRAPHS OF COMMUTATOR POSETS

• Varmazyar, Rezvan (Department of Mathematics, Khoy Branch, Islamic Azad University)
• Accepted : 2018.02.10
• Published : 2018.03.25
• 153 5

#### Abstract

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).

#### Keywords

Annihilator graph;zero-divisor graph;commutator poset

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