[PDF] Top 20 A generalization of zero-divisor graphs

... the zero-divisor graph of a ring in his 1988 paper ...of zero-divisor graphs ...with zero by DeMeyer et ...the zero-divisor graphs from different ... See full document

... of zero- ...non- zero zero divisors of R and for distinct u, v ∈ Z (R) * , the vertices u and v are adjacent if and only if uv = 0 ...bipartite zero divisor ... See full document

... We encourage the reader to see the special issue of MATCH Communications in Mathematical and in Computer Chemistry for more information on this topic [2].. In this article we discuss th[r] ... See full document

... of zero-divisor graphs of the integers modulo ...the zero-divisor graphs of five commutative rings; ℤ 10 , ℤ 12 , ℤ 14 , ℤ 15 , ℤ 16 , ... See full document

... We conclude this section by posing a question on the isomorphism of the rings of 3-zero-divisor hypergraphs. In [6], it is shown that for any finite reduced commutative rings A and B which are not fields, ... See full document

... a divisor graph is a divisor graph (proposition 3. Complete graphs and bipartite graphs are divisor graphs (proposition ...a divisor graph if and only if there is an ... See full document

... of zero-divisor graph of a commutative ring was introduced by Beck [1], but this work was mostly concerned with colorings of ...The zero-divisor graphs of commuta- tive rings have been ... See full document

... cordial graphs were discussed in [6, 7, 8, ...to zero-divisors of a commutative ring was introduced by ...all zero-divisors in R and Z ∗ (R) = Z(R)\{0}. The zero-divisor graph of R is ... See full document

... on zero divisor ...studying zero divisor graphs of trivial ...the zero-divisor graph for the ring of Gaussian integers modulo n, ... See full document

... vertices a and b if and only if a 6= b and ab = 0. Thus Γ(R) is the empty graph if and only if R is an integral domain. The concept of zero-divisor graphs has been studied extensively by many ... See full document

... In [4], the authors proved that for any commutative ring R, Γ(R) ∼ = Γ(T (R)) where T (R) is the quotient ring of R. Here, by the same method as [4], we extend this fact to the reduced right Ore rings. Theorem 2.2. Let R ... See full document

... In 1988, Beck [10] introduced the notion of coloring of a commutative ring R. Let G be a simple graph whose vertices are the elements of R and two vertices x and y are adjacent if xy = 0. The graph G is known as the ... See full document

... If P is'a localizable prime ideal of the Noetherian ring R, "Ie shall denote the partial quotient ring of.. above by Rp, and call.[r] ... See full document

... Varatharajan et al. [12] introduced the concept of divisor cordial labeling. Vaidya and shah [11] proved that some star and bistars related graphs are divisor cordial labeling. Deshmukh and Shaikh ... See full document

... cordial graphs under some conditions. Every divisor cordial graphs need not be vertex odd divisor cordial ...odd divisor cordial graphs need not be divisor cordial ... See full document

... of graphs is an active research area and it has been widely studied by several ...of graphs have been applied in the fields such as circuit design, communication network, coding theory, and ... See full document

... of divisor cordial labeling of ...square divisor cordial labeling of graph. The square divisor cordial labeling of various types of graph is presented in ... See full document

... By a graph, we mean a finite, undirected graph without loops and multiple edges, for terms not defined here, we refer to Harary [4]. For standard terminology and notations related to number theory we refer to Burton [2] ... See full document

... a divisor cordial labeling is called a divisor cordial ...splitting graphs of star K 1,n and bistar B n n , are divisor cordial ...admit divisor cordial labeling ... See full document

... sum divisor cordial labeling of a graph G with vertex set V is a bijection f from V(G) to {1,2,…, |V(G)|} such that an edge uv is assigned the label 1 if 2 divides f(u)+f(v) and 0 otherwise, then the number of ... See full document