The notion of a zero-divisor graph Γ ( R ) of a commutative ring R was first introduced by Beck in [1] and was further investigated in [2], where the authors were interested in

In many cases zero divisor graph of equivalence classes of zero divisors in a commutative ring R is finite when the zero divisor graph is infinite.. Another important aspect of

Key words: Commutative ring, Zero divisors, Zero divisor graph Triangle graph, Bipartite Graph, Complete Bipartite

D avid F.Anderson and Philip S.Livingston studied the properties of the zero divisor graph of a commutative ring.. We recall several results of zero divisor graph, total graphs

The zero divisor graph of a ring R, denoted by Γ(R), is the simple graph associated to R such that its vertex set consists of all its nonzero divisors and that two distinct vertices

Later in the paper [2], the authors define the zero-divisor graph Γ(R) where the set of vertices is taken to be Z ∗ (R).The zero-divisor graph of a commutative ring has also

Motivated by the study of exact zero-divisor graph of commutative rings studied in [ 5 ] and [ 6 ], we define exact annihilating-ideal graph EAG(R) of a commutative ring R to be

We note that for a commutative ring R, its zero-divisor graph is finite if and the ring R is finite or an integral domain ([3], Theorem 2.2)..

Let

Key words and phrases: commutative ring, zero-divisor graph, nilradical graph, non-nilradical graph, chromatic number, planar graph, energy of a graph.... two sets such that

Beck, in his work in [1], associated to any commutative ring R its zero divisor graph G ( R ) whose vertices are the zero divisors of R (including an element 0 of R ) and

In [5], Anderson and Livingston proved that the graph Γ ( ) is connected with diameter at most 3. The zero divisor graph of a commutative ring has been studied extensively by

By using the results in this article and examining the graphs found in [ 11 ], one can determine the upper dimension of all zero divisor graphs of a commutative ring with up to

In this paper, we prove that certain classes of zero-divisor graphs of commutative rings are sum cordial.. Keywords: zero-divisor graph, cordial labeling, sum

Smith obtained all commutative rings whose zero divisor graph has genus at most one [23, Theorem 3.6.2].. Note that the zero divisor graph Γ( R ) is a subgraph of AG(

LaGrange, Commutative Boolean monoids, reduced rings, and the compressed zero-divisor graph, J. Macdonald, Introduction to commutative algebra,

In this paper, we prove that certain classes of zero-divisor graphs of commutative rings are SD-prime cordial graphs1. Keywords: zero-divisor graphs; SD-prime

The seismic refraction profiling method measures the velocity of refracted seismic waves through the overburden and rock material and allows an assessment of the