THE ARMENDARIZ GRAPH OF A RING
Journal Title: Discussiones Mathematicae - General Algebra and Applications - Year 2018, Vol 38, Issue 2
Abstract
In this paper we initiate the study of Armendariz graph of a commutative ring R and investigate the basic properties of this graph such as diameter, girth, domination number, etc. The Armendariz graph of a ring R, denoted by A(R), is an undirected graph with nonzero zero-divisors of R[x] (i.e., Z(R[x])∗) as the vertex set, and two distinct vertices f(x) = Pni=0aix i andg(x) = Pmj=0bjxj are adjacent if and only if aibj = 0, for all i, j. It is shownthat A(R), a subgraph of Γ(R[x]), the zero divisor graph of the polynomial ring R[x], have many graph properties in common with Γ(R[x]). Keywords: Armendariz property, diameter, girth, zero-divisor graph. 2010 Mathematics Subject Classification: 05C12, 05C25.
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