There is a natural graph associated to the zero-divisors of a commutative semiring with non-zero identity. In this article we essentially study zero-divisor graphs with respect to primal and non-primal ideals of a commutative semiring R and investigate the interplay between the semiring-theoretic properties of R and the graph-theoretic properties of ΓI(R) for some ideal I of R. We also show tha...

In this paper we consider, for a finite commutative ring R, the wellstudied zero-divisor graph Γ(R) and the compressed zero-divisor graph Γc(R) of R and a newly-defined graphical structure — the zero-divisor lattice Λ(R) of R. We give results which provide information when Γ(R) ∼= Γ(S), Γc(R) ∼= Γc(S), and Λ(R) ∼= Λ(S) for two finite commutative rings R and S. We also provide a theorem which sa...

Let F/Fq be an algebraic function field of genus g defined over a finite field Fq. We obtain new results on the existence, the number and the density of dimension zero divisors of degree g− k in F/Fq where k is an integer ≥ 1. In particular, for q = 2, 3 we prove that there always exists a dimension zero divisor of degree γ − 1 where γ is the q-rank of F and in particular a non-special divisor ...

The detour pebbling number of a graph \(G\) is the least positive integer \(f^{*}(G)\) such that these pebbles are placed on vertices \(G\), we can move pebble to target vertex by sequence moves each taking two off and placing one an adjacent using path. In this paper, compute for commutative ring zero-divisor graphs, sum product zero divisor graphs.