On Distance Related Spectrum Of Nil-Graph Of Ideals Of Commutative Rings

Abstract

Let R be a commutative ring with identity and Nil(R) be the ideal of all nilpotent elements of R. Let I(R) = {I: I is a non-trivial ideal of R and there exists a non-trivial ideal J such that IJ⊆Nil(R).} The nil-graph of ideals of R is defined as the graph AG_N (R) whose vertex set is the set I(R) and two distinct vertices I and J are adjacent if and only if IJ⊆Nil(R). In this paper, we determine distance signless Laplacian and distance Laplacian spectrum of AG_N (R) when R is reduced.