Computing metric dimension of compressed zero divisor graphs associated to rings

DOI10.2478/ausm-2018-0023zbMath1411.13003OpenAlexW2919537091WikidataQ128286999 ScholiaQ128286999MaRDI QIDQ1737405

M. Imran Bhat, Shariefuddin Pirzada

Publication date: 27 March 2019

Published in: Acta Universitatis Sapientiae. Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2478/ausm-2018-0023

zbMATH Keywords

equivalence classesmetric dimensionzero-divisor graphcompressed zero-divisor graph

Mathematics Subject Classification ID

Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Distance in graphs (05C12) Graph labelling (graceful graphs, bandwidth, etc.) (05C78) Ideals and multiplicative ideal theory in commutative rings (13A15) Divisibility and factorizations in commutative rings (13A05)

Related Items (13)

Fault-tolerant metric dimension of zero-divisor graphs of commutative rings ⋮ ON THE STRONG METRIC DIMENSION OF A TOTAL GRAPH OF NONZERO ANNIHILATING IDEALS ⋮ Strong resolving graph of a zero-divisor graph ⋮ Twin-free cliques in annihilator graphs of commutative rings ⋮ Co-unit graphs associated to ring of integers modulo \(n\) ⋮ The forcing metric dimension of a total graph of nonzero annihilating ideals ⋮ On the metric dimension of strongly annihilating-ideal graphs of commutative rings ⋮ Metric and strong metric dimension in cozero-divisor graphs ⋮ Eigenvalues of zero-divisor graphs of finite commutative rings ⋮ On zero divisor graphs of the rings \(Z_n\) ⋮ On graphs with same metric and upper dimension ⋮ On strong metric dimension of zero-divisor graphs of rings ⋮ Subspace-based nonzero component graph of a finite dimensional vector space

Cites Work

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• Commutative Boolean monoids, reduced rings, and the compressed zero-divisor graph
• On zero-divisor graphs of small finite commutative rings
• Some remarks on the compressed zero-divisor graph
• Coloring of commutative rings
• The zero-divisor graph of a commutative ring
• Beck's coloring of a commutative ring
• Resolvability in graphs and the metric dimension of a graph
• Rings of order \(p^5\). II: Local rings
• On the zero-divisor graph of a commutative ring
• Landmarks in graphs
• On locating numbers and codes of zero divisor graphs associated with commutative rings
• ON GRAPHS ASSOCIATED WITH MODULES OVER COMMUTATIVE RINGS
• Locating sets and numbers of graphs associated to commutative rings
• On the metric dimension of a zero-divisor graph
• A Zero Divisor Graph Determined by Equivalence Classes of Zero Divisors
• CYCLES AND SYMMETRIES OF ZERO-DIVISORS
• An Ideal-Based Zero-Divisor Graph of a Commutative Ring
• Zero-Divisor Graph with Respect to an Ideal
• On Metric Generators of Graphs

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