Let R be a commutative ring with nonzero identity and let id="M2"> Z its set of zero divisors. The zero-divisor graph id="M3"> is the id="M4"> ? vertex id="M5"> V = ? , wh...

For any commutative ring R that is not a domain, there is a zerodivisor graph, denoted Γ(R), in which the vertices are the nonzero zero-divisors of R and two distinct vertices x and y are joined by an edge exactly when xy = 0. In [Sm2], Smith characterized the graph structure of Γ(R) provided it is infinite and planar. In this paper, we give a ring-theoretic characterization of R such that Γ(R)...

In this paper we will investigate the interactions between the zero divisor graph, the annihilator class graph, and the associate class graph of commutative rings. Acknowledgements: We would like to thank the Center for Applied Mathematics at the University of St. Thomas for funding our research. We would also like to thank Dr. Michael Axtell for his help and guidance, as well as Darrin Weber f...

An assignment of intergers to the vertices a graph subject certain constraints is called vertex labeling src=image/13424638_01.gif>. Different types techniques are used in field coding theory, cryptography, radar, missile guidance, src=image/13424638_02.gif>-ray crystallography etc. A DCL bijective function src=image/13424638_03.gif> from node set src=image/13424...