The edge chromatic number of ΓI (R)

Abstract

For a commutative ring R and an ideal I of R, the ideal-based zero-divisor graph is the undirected graph ΓI (R) with vertices {x ∈ R−I : xy ∈ I for some y ∈ R−I}, where distinct vertices x and y are adjacent if and only if xy ∈ I. In this paper, we discuss the nature of the edges of ΓI (R). We also find the edge chromatic number for the graph ΓI (R).