On locating numbers and codes of zero divisor graphs associated with commutative rings

DOI10.1142/S0219498816500146zbMath1331.13005MaRDI QIDQ2788759

Shane P. Redmond, Rameez Raja, Shariefuddin Pirzada

Publication date: 22 February 2016

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

zbMATH Keywords

ringzero-divisor graphzero-divisorlocating numberlocating code

Mathematics Subject Classification ID

General commutative ring theory (13A99)

Related Items (20)

On some applications related with algebraic structures through different well known graphs ⋮ Fault-tolerant metric dimension of zero-divisor graphs of commutative rings ⋮ Metric dimension of complement of annihilator graphs associated with commutative rings ⋮ On the metric dimension of a zero-divisor graph ⋮ Metric and upper dimension of zero divisor graphs associated to commutative rings ⋮ The metric dimension of annihilator graphs of commutative rings ⋮ Computing metric dimension of compressed zero divisor graphs associated to rings ⋮ On the metric dimension of strongly annihilating-ideal graphs of commutative rings ⋮ Unnamed Item ⋮ Upper dimension and bases of zero-divisor graphs of commutative rings ⋮ Metric and strong metric dimension in cozero-divisor graphs ⋮ Unnamed Item ⋮ Fixing number and metric dimension of a zero-divisor graph associated with a ring ⋮ On the strong metric dimension of annihilator graphs of commutative rings ⋮ Unnamed Item ⋮ Annihilating-ideal graphs of commutative rings ⋮ Group-annihilator graphs realised by finite abelian groups and its properties ⋮ On zero divisor graphs of the rings \(Z_n\) ⋮ On graphs with same metric and upper dimension ⋮ When metric and upper dimensions differ in zero divisor graphs of commutative rings

Cites Work

• Unnamed Item
• On zero-divisor graphs of small finite commutative rings
• Coloring of commutative rings
• The zero-divisor graph of a commutative ring
• Beck's coloring of a commutative ring
• Zero-divisor graphs, von Neumann regular rings, and Boolean algebras.
• Locating sets and numbers of graphs associated to commutative rings
• CYCLES AND SYMMETRIES OF ZERO-DIVISORS
• Cut Vertices and Degree One Vertices of Zero-Divisor Graphs
• An Ideal-Based Zero-Divisor Graph of a Commutative Ring
• THE ZERO-DIVISOR GRAPH OF VON NEUMANN REGULAR RINGS

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