Zero-Divisor Graphs
On zero-divisor graphs of quotient rings and complemented zero-divisor graphs
... the zero-divisor graph of R, denoted by Γ(R), is an undirected simple graph that its vertices are all nonzero zero-divisors of R in which any two vertices x and y are adjacent if and only if either ...
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Construction of Zero Divisor Graphs of Rings
... on zero divisor graphs on commutative ...of zero divisor graph are the non-zero zero-divisor of the ...of zero- divisor of 𝑅 and Z* 𝑅 = 𝑍 𝑅 − 0 , then ...
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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 ...
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$C_4$-free zero-divisor graphs
... 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 ...
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Zero divisor graphs of posets
... Further, this concept of zero divisor graphs is well studied in alge- braic structures such as rings, semigroups; see Anderson et. al. [1, 2], F. DeMeyer et. al. [14, 15], LaGrange [31, 32], Redmond ...
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Energy and Wiener Index of Zero-Divisor Graphs
... 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] ...
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The k Zero Divisor Hypergraph of a Commutative Ring
... on zero-divisor graphs, the edges are defined to be between the distinct nonzero zero-divisors in order to construct a graph with no ...the zero-divisor graph of a ...
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Vol 8, No 7 (2017)
... Planarity is of great significance from a theoretical point of view [3, 4]. In addition planarity and other related concepts are useful in many practical situations [4, 5]. For instance, in the design of a ...
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INDEPENDENCE AND CLIQUE POLYNOMIALS OF ZERO-DIVISOR GRAPH OF THE INTEGER MODULO n (ℤ𝒏)
... 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 , ...
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On the Cozero Divisor Graphs of Commutative Rings
... 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 ...
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On the genus of the annhilator graph of a commutative ring
... Many research articles have appeared on the genus of zero divisor graphs of commutative rings. In particular, there are many papers [1, 2, 9, 15, 24], where the planarity of ...
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Several result on SD-prime cordial graphs
... 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 ...
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Properties of extended ideal based zero divisor graph of a commutative ring
... the zero divisor graph of ring and initiated the study of the relation between ring- theoretic properties and graph theoretic ...the zero divisor graphs of commutative rings have ...
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On the zero forcing number of graphs and their splitting graphs
... Proof. Assume that we have a zero forcing set Z consisting of 2n − 3 vertices. Then the number of white vertices in Z is 2n + 2 − (2n − 3) = 5. Consider the five white vertices in S(Γ). Consider the case when ...
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Vol 7, No 2 (2016)
... Istvan Beck first introduce the concept of relating a commutative ring to a graph. This paper forms a new bridge between graph theory and the algebraic concept of ring R. Here R denote a commutative ring with identity. ...
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Some New Results on Sum Divisor Cordial Graphs
... By a graph, we mean a finite undirected graph without loops or multiple edges. For standard terminology and notations related to graph theory we refer [4] . A labeling of graph is a map that carries the graph elements to ...
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Some New Families of Sum Divisor Cordial Graphs
... of divisor cordial labeling of graphs. The concept of sum divisor cordial labeling was introduced by Lourdusamy et ...sum divisor cordial ...
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Some Star and Bistar Related Divisor Cordial Graphs
... Definition 1.6. Let G = ( ( ), ( )) V G E G be a simple graph and f : → {1, 2,... | ( ) |} V G be a bijection. For each edge uv , assign the label 1 if either f u ( ) | ( ) f v or f v f u ( ) | ( ) and the label 0 if f u ...
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Some Star Related Vertex Odd Divisor Cordial Labeling of Graphs
... labeling, divisor cordial ...the divisor cordial labeling.The divisor cordial labeling of various types of the graph is presented in ...odd divisor cordial ...
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Efficient Zero Ring Labeling of Graphs
... called zero ring ...efficient zero ring labeling of graphs. In this study, the zero ring that will be used in the vertex labelings is the zero ring M 2 0 ( Z n ...
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