Locating sets and numbers of graphs associated to commutative rings

DOI10.1142/S0219498814500479zbMath1296.05090MaRDI QIDQ2874711

Rameez Raja, Shane P. Redmond, Shariefuddin Pirzada

Publication date: 8 August 2014

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

zbMATH Keywords

commutative ringzero-divisor graphlocating setlocating number

Mathematics Subject Classification ID

Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) (05C69) General commutative ring theory (13A99) Combinatorial aspects of commutative algebra (05E40)

Related Items (20)

Fault-tolerant metric dimension of zero-divisor graphs of commutative rings ⋮ Strong resolving graph of a zero-divisor graph ⋮ 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 ⋮ On locating numbers and codes of zero divisor graphs associated with commutative rings ⋮ 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 graphs with same metric and upper dimension ⋮ When metric and upper dimensions differ in zero divisor graphs of commutative rings ⋮ On strong metric dimension of zero-divisor graphs of rings ⋮ Subspace-based nonzero component graph of a finite dimensional vector space

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
• On the zero-divisor graph of a commutative ring
• RECOVERING RINGS FROM ZERO-DIVISOR GRAPHS
• 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
• THE ZERO-DIVISOR GRAPH OF VON NEUMANN REGULAR RINGS
• Some Remarks on the Graph Γ_I(R)

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