Nilpotent Graph

Abstract

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.

Keywords

• nilpotent graph
• spectrum
• laplacian spectrum
• signless laplacian spectrum