Abstract
The nilpotent graph is a graph’s structure motivated by the characteristics of some elements of a ring. If G is a graph, G(N) is a nilpotent graph in which the set of all non-nilpotent elements of a ring taken as a vertex set. For each x, y in R\ il(R), x and y are said to be connected or adjacent to an edge, if the sum of the vertices x and y is equal to the nilpotent element in the ring. This research aims to explain how to construct a nilpotent graph G(N) from a commutative ring. The results of this research are the characteristic of the nilpotent graph of a ring Zn for n prime numbers, a nilpotent graph for the ring Z 2 k, and ring Zn with n = 6m where 1 ≤ m < 5 can create 3 nilpotent subgraphs, they are a complete subgraph (km ) and 2 regular subgraphs in which the degree of vertices is equal to m.
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