In this paper, two outwardly different graphs, namely, the zero-divisor graph [Formula: see text] and comaximal of ring all real-valued continuous functions having countable range, defined on any zero-dimensional space text], are investigated. It is observed that these graphs exhibit resemblance, so far as diameters, girths, connectedness, triangulatedness or hypertriangulatedness concerned. Ho...

We determine the number of edges of the zero-divisor graph of the direct product of finitely many finite non-commutative rings or semigoups.

The aim of this article to follow the properties zero-divisor graph special idealization ring. We study wiener index zero-divisors some ring R(+)M and find clique number Γ(R(+)M) is ω (Γ(R(+)M)) = |M| − 1, where R an integral domain. also discuss when are Hamiltonian graph.

In a manner analogous to a commutative ring, the L-ideal-based L-zero-divisor graph of a commutative ring R can be defined as the undirected graph Γ(μ) for some L-ideal μ of R. The basic properties and possible structures of the graph Γ(μ) are studied.

In a manner analogous to a commutative ring, the idealbased zero-divisor graph of a commutative semiring R can be defined as the undirected graph ΓI(R) for some ideal I of R. The properties and possible structures of the graph ΓI (R) are studied.

L-zero-divisor graphs of L-commutative rings have been introduced and studied in [5]. Here we consider L-zero-divisor graphs of a finite direct product of L-commutative rings. Specifically, we look at the preservation, or lack thereof, of the diameter and girth of the L-zirodivisor graph of a L-ring when extending to a finite direct product of L-commutative rings.

Let R be a commutative ring and let ? Z n the zero divisor graph of id="M2"> R , whose vertices are nonzero divisors id="M3"> such that two id="M4"> u , v adjacen...

Let R be a commutative ring with nonzero identity and Z(R) its set of zero-divisors. The new extension the zero-divisor graph $$\widetilde{\Gamma }(R)$$ vertices $$Z(R)^{\star }$$ , two distinct x y are adjacent if only $$xy=0$$ or $$x+y\in Z(R)$$ . In this article, we study, in general case, For any R, provide sufficient necessary conditions for }(R[x_1,\dots x_n])$$ to complete. At last, pres...