THE METRIC DIMENSION OF THE ANNIHILATING-IDEAL GRAPH OF A FINITE COMMUTATIVE RING

DOI10.1017/S0004972720001239zbMath1464.05176arXiv2006.10501OpenAlexW3158407185MaRDI QIDQ4989462

David Dolžan

Publication date: 25 May 2021

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2006.10501

zbMATH Keywords

annihilating-ideal graphmetric dimensionfinite ring

Mathematics Subject Classification ID

Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Principal ideal rings (13F10) Distance in graphs (05C12) Ideals and multiplicative ideal theory in commutative rings (13A15)

Related Items (6)

ON THE STRONG METRIC DIMENSION OF A TOTAL GRAPH OF NONZERO ANNIHILATING IDEALS ⋮ Strong resolving graph of a zero-divisor graph ⋮ Computing the strong metric dimension for co-maximal ideal graphs of commutative rings ⋮ Twin-free cliques in annihilator graphs of commutative rings ⋮ The metric dimension of the zero-divisor graph of a matrix semiring ⋮ The forcing metric dimension of a total graph of nonzero annihilating ideals

Cites Work

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• Coloring of commutative rings
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• Resolvability in graphs and the metric dimension of a graph
• Landmarks in graphs
• On the Commuting Graph of Dihedral Group
• Some Results on Annihilating-ideal Graphs
• On the Complexity of Metric Dimension
• On the metric dimension of a zero-divisor graph
• THE ANNIHILATING-IDEAL GRAPH OF COMMUTATIVE RINGS I
• THE ANNIHILATING-IDEAL GRAPH OF COMMUTATIVE RINGS II
• THE ANNIHILATING-IDEAL GRAPH OF A RING
• Classifying annihilating-ideal graphs of commutative artinian rings
• Annihilating-ideal graphs of commutative rings
• On the connectivity of the annihilating-ideal graphs
• The (Weighted) Metric Dimension of Graphs: Hard and Easy Cases
• Domination number in the annihilating-ideal graphs of commutative rings
• The Metric Dimension of the Total Graph of a Finite Commutative Ring
• The Classification of the Annihilating-Ideal Graphs of Commutative Rings
• On Metric Generators of Graphs
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