ABSTRACT:
The idempotent divisor graph of a commutative ring is a graph with vertices set in * = -{0}, and two distinct vertices d1 ,d2 are adjacent if and only if = e. For some non-unit idempotent element e2 = e ∊ , it is denoted by ( ) . In this paper, we find some basic properties of this graph when a ring is direct product of field order 2 and local ring of nilpotency 2. As well as we fined The Zagreb index of this graph.
Key word: idempotent divisor graph, zero divisor graph, direct product, Zagreb index of graph.
