Results 61 to 70 of about 22,120 (235)
Eulerian and pancyclic zero-divisor graphs of ordered sets
AKCE International Journal of Graphs and CombinatoricsIn this paper, we determine when the zero-divisor graph of a special class of a finite pseudocomplemented poset is Eulerian. Also, we deal with Hamiltonian, vertex pancyclic, and edge pancyclic properties of the complement of a zero-divisor graph of ...
Nilesh Khandekar, Vinayak Joshi
doaj +1 more source
The diameter of a zero divisor graph
Journal of Algebra, 2006 AbstractLet R be a commutative ring and let Z(R)∗ be its set of nonzero zero divisors. The set Z(R)∗ makes up the vertices of the corresponding zero divisor graph, Γ(R), with two distinct vertices forming an edge if the product of the two elements is zero.
openaire +2 more sources
The Zero Divisor Graph of the Ring Z_(2^2 p)
ARO-The Scientific Journal of Koya University, 2016 In this paper, we consider the crossing number and the chromatic number of the zero divisor graph Γ(Z_(2^2 p)) to show that this type of zero divisor graphs is bipartite graph, and the smallest cycle in Γ(Z_(2^2 p)) is of length four this implies that ...
Nazar H. Shuker, Payman A. Rashed
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Strong External Difference Families and Classification of α $\alpha $‐Valuations
Journal of Combinatorial Designs, EarlyView.ABSTRACT One method of constructing (a2+1,2,a,1) $({a}^{2}+1,2,a,1)$‐SEDFs (i.e., strong external difference families) in Za2+1 ${{\mathbb{Z}}}_{{a}^{2}+1}$ makes use of α $\alpha $‐valuations of complete bipartite graphs Ka,a ${K}_{a,a}$. We explore this approach and we provide a classification theorem which shows that all such α $\alpha $‐valuations ...
Donald L. Kreher +2 more
wiley +1 more source
Fault-tolerant metric dimension of zero-divisor graphs of commutative rings
AKCE International Journal of Graphs and Combinatorics, 2021 Let R be a commutative ring with identity. The zero-divisor graph of R denoted by is an undirected graph where is the set of non-zero zero-divisors of R and there is an edge between the vertices z1 and z2 in if A set of vertices S resolves a graph G if ...
Sahil Sharma, Vijay Kumar Bhat
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Some results on the total zero-divisor graph of a commutative ring
Arab Journal of Mathematical SciencesPurposeThe purpose of this paper is to characterize a commutative ring R with identity which is not an integral domain such that ZT(R), the total zero-divisor graph of R is connected and to determine the diameter and radius of ZT(R) whenever ZT(R) is ...
S. Visweswaran
semanticscholar +1 more source
Modeling General Asymptotic Calabi–Yau Periods
Fortschritte der Physik, EarlyView.Abstract In the quest to uncovering the fundamental structures that underlie some of the asymptotic Swampland conjectures the authors initiate the general study of asymptotic period vectors of Calabi–Yau manifolds. The strategy is to exploit the constraints imposed by completeness, symmetry, and positivity, which are formalized in asymptotic Hodge ...
Brice Bastian +2 more
wiley +1 more source
Note on Ideal Based Zero-Divisor Graph of a Commutative Ring
Discussiones Mathematicae - General Algebra and Applications, 2017 In this paper, we consider the ideal based zero divisor graph ΓI(R) of a commutative ring R. We discuss some graph theoretical properties of ΓI(R) in relation with zero divisor graph.
Mallika A., Kala R., Selvakumar K.
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Computing Wiener and Hyper-Wiener Indices of Zero-Divisor Graph of ℤℊ3×ℤI1I2
Journal of Function Spaces, 2022 Let S=ℤℊ3×ℤI1I2 be a commutative ring where ℊ,I1 and I2 are positive prime integers with I1≠I2. The zero-divisor graph assigned to S is an undirected graph, denoted as YS with vertex set V(Y(S)) consisting of all Zero-divisor of the ring S and for any c,
Yonghong Liu +4 more
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Commutative rings with ideal based zero divisor graph of orders 12,13 and 14 [PDF]
Al-Rafidain Journal of Computer Sciences and MathematicsAn recent years, several studies have emerged on the graphs for commutative rings. Researchers have investigated ideal based zero-divisor graphs linked to commutative rings, delving into the characteristics of these graphs.
Raad Shukur, Husam Mohammad
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