… corresponding graphs. The hope is that the graph-theoretic properties of the graph from the
ring will help us better understanding the ring-theoretic properties of the ring. Not only have …

… ring instead of zero divisors. The unit graph of a ring is such a graph, which is the topics in this
paper… This paper concerns with diameters of unit graphs of rings. The study of diameters of …

… ring R ≅ R 1 × R 2 × ⋯ × R n , where R i is a local ring with maximal ideal M i and n ≥ 3 , we
prove that the graph Γ U … We also discuss all the finite rings R such that the graph Γ U ( R ) is …

… a ring with unity. In this paper, we introduce a new graph associated with R called the
simple-intersection graph … the algebraic properties of R, and the graph properties of GS(R) such as …

… graphs that are defined on rings, that is, the graphs defined such that their vertex sets are the
ring … condition given in the Cayley graph with respect to some symmetric subset of the ring. …

… nontrivial topology of spatial graphs as embeddings in … graphs with no loop such as
stars or brushes have only a trivial topology, while graphs with loops such as rings, multiple-rings …

… Recently, it has been very popular to consider graphs associated to rings (the zero-divisor
graph, the Cayley graph, etc.). In the present paper, we study the directed graph defined by …

… This investigation of colorings of a commutative ring … graphs from these multirings. Indeed,
we connect the special category of hyperstructures to graphs via derivable zero-divisor graphs …

… χ is a ring homomorphism from the strong ring to the integers and that the Kuenneth formula
holds: the map from the graph to its Poincaré polynomial p(G) is a ring homomorphism p(G + …

… the strong metric dimension of zero-divisor graph Γ(R) associated to a ring R. This is done by
… resolving graph Gsr. We find the strong metric dimension of zero-divisor graphs of the ring …