In this article, we introduce the concept of nilpotent graph of a finite commutative ring. The set of all non nilpotent elements of a ring is taken as the vertex set and two vertices are adjacent if and only if their sum is nilpotent. We discuss some graph theoretic properties of nilpotent graph.
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Basnet, Dhiren Kumar; Sharma, Ajay; and Dutta, Rahul
Theory and Applications of Graphs: Vol. 8
, Article 2.
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol8/iss1/2