Results 21 to 30 of about 1,460,755 (212)
A graph-theoretic approach to ring analysis: Dominant metric dimensions in zero-divisor graphs [PDF]
HeliyonThis article investigates the concept of dominant metric dimensions in zero divisor graphs (ZD-graphs) associated with rings. Consider a finite commutative ring with unity, denoted as R, where nonzero elements x and y are identified as zero divisors if ...
Nasir Ali +4 more
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The Zero Divisor Graph of the Ring Z_(2^2 p) [PDF]
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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Note on Ideal Based Zero-Divisor Graph of a Commutative Ring [PDF]
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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A Study on the Structure of Ideal-Based Non-Zero Divisor Graphs Associated with Zn [version 1; peer review: 2 approved] [PDF]
F1000ResearchBackground The study of algebraic structures through graph-theoretic representations provides a powerful visual and combinatorial framework for analyzing ring-theoretic properties. The ideal-based non-zero divisor graph ∅ I ( Z n ) , constructed from the
Ali Abd Aubad, Sameer Kadem
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A note on the zero divisor graph of a lattice [PDF]
Transactions on Combinatorics, 2014 Let $L$ be a lattice with the least element $0$. An element $xin L$ is a zero divisor if $xwedge y=0$ for some $yin L^*=Lsetminus left{0right}$. The set of all zero divisors is denoted by $Z(L)$.
T. Tamizh Chelvam , S. Nithya
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Hosoya and Wiener Index of Zero-Divisor Graph of Z pm q2 [PDF]
Zanco Journal of Pure and Applied Sciences, 2019 In this work, we study zero-divisor graph of the ring Zpmq2 and give some properties of this graph. Furthermore we find Hosoya polynomial and Wiener index for this graph.
Nazar H. Shuker +2 more
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Frequency Assignment Model of Zero Divisor Graph [PDF]
Journal of Applied Mathematics, 2021 Given a frequency assignment network model is a zero divisor graph Γ=V,E of commutative ring Rη, in this model, each node is considered to be a channel and their labelings are said to be the frequencies, which are assigned by the L2,1 and L3,2,1 labeling
R. Radha, N. Mohamed Rilwan
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Zero-divisor graphs and zero-divisor functors
Journal of Algebra and Its Applications, 2023 Inspired by a very recent work of A. Đurić, S. Jevđenić and N. Stopar, we introduce a new definition of zero-divisor graphs attached to rings that includes all of the classical definitions already known in the literature. We provide an interpretation of such graphs by means of a functor that we call zero-divisor functor and which is associated with a ...
Enrico Sbarra, Maurizio Zanardo
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Total perfect codes in graphs realized by commutative rings [PDF]
Transactions on Combinatorics, 2022 Let $R$ be a commutative ring with unity not equal to zero and let $\Gamma(R)$ be a zero-divisor graph realized by $R$. For a simple, undirected, connected graph $G = (V, E)$, a {\it total perfect code} denoted by $C(G)$ in $G$ is a subset $C(G ...
Rameez Raja
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Dynamic multi‐objective optimisation of complex networks based on evolutionary computation
IET Networks, EarlyView., 2022 Abstract As the problems concerning the number of information to be optimised is increasing, the optimisation level is getting higher, the target information is more diversified, and the algorithms are becoming more complex; the traditional algorithms such as particle swarm and differential evolution are far from being able to deal with this situation ...
Linfeng Huang
wiley +1 more source