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RISTotal graphs of Polynomial Rings and Rings of fractions
Let R be a commutative ring. The total graph of R, denoted by T(Γ(R)), is a graph
with all elements of R as vertices, and two distinct vertices x, y ∈ R are adjacent if and
only if x + y ∈ Z(R), where Z(R) ...
On the cozero-divisor graphs of commutative rings
Let R be a commutative ring with non-zero identity. The
cozero-divisor graph of R, denoted by \\Gamma'(R), is a graph
with vertices in W^*(R), which is the set of all non-zero and
non-unit ...
The Cozero-divisor Graph of a Commutative Ring
For a commutative ring R with non-zero identity, we denote the
set of non-zero element x in R with xR neq R by
W^*(R). So W^*(R) is the set of non-units of R. In this paper,
we introduced the ...
The Annihilating-Ideal graph of A Lattice
Let L be a lattice with a least element called zero and denoted by 0.The annihilating-ideal graph of L , denoted by AG(L), is a graph whose vertex-set is the set of all nontrivial ideals of L and, for ...
Distance between spectra of graphs with respect to normalized laplacian spectra
Given a graph G, the normalized Laplacian associated with the
graph G, denoted by L(G), was introduced by F.R.K. Chung and has been
intensively studied in the last 20 years. Richard Brualdi proposed in [7] ...
Zero-divisor graphs of extension rings
Let R be an associative ring with two-sided multiplicative identity. In this talk, in the
case that R is a commutative a-compatible ring, we determine the diameter (and girth)
of the zero-divisor graphs ...
On the toroidal and projactive Jacobson graphs
Let R be a commutative ring with non-zero identity and J(R) be the Jacobson radical of R. The Jacobson graph of R denoted by J_R is a graph with vertex-set R\\J(R) such that two distinct vertices a and b in R\\J(R) are ...
On the regular graphs associated to commutative rings
Let R be a commutative ring. The regular digraph of ideals of R denoted by T(R) is a digraph whose vertex-set is the set of all non-trivial ideals of R and for every two distinct vertices I and J there is an arc from I ...
On the zero-divisor graphs of posets
In this paper we determine the cut vertices in the zero-divisor graphs of posets. Also we investigate some properties of zero-divisor graph of the product of two posets.
On end-regular, planar and outer planar of zero-divisor graphs of posets
In this talk we study the posets with end-regular zero-divisor graph. Also we investigate the zero-divisor graph of the product of two posets. In particular we determine all posets with planar and outer planar zero-divisor ...