On strong metric dimension of zero-divisor graphs of rings

DOI10.11568/kjm.2019.27.3.563zbMath1427.13003OpenAlexW2978695432MaRDI QIDQ5204514

M. Imran Bhat, Shariefuddin Pirzada

Publication date: 4 December 2019

Full work available at URL: http://journal.kkms.org/index.php/kjm/article/view/702/479

zbMATH Keywords

metric dimensionzero-divisor graphstrong metric dimension

Mathematics Subject Classification ID

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

Related Items (max. 100)

Some aspects of zero-divisor graphs for the ring of Gaussian integers modulo \(2^n\) ⋮ Fault-tolerant metric dimension of zero-divisor graphs of commutative rings ⋮ Strong resolving graph of a zero-divisor graph ⋮ Computing the strong metric dimension for co-maximal ideal graphs of commutative rings ⋮ The metric dimension of the zero-divisor graph of a matrix semiring ⋮ Co-unit graphs associated to ring of integers modulo \(n\) ⋮ Unnamed Item ⋮ Metric and strong metric dimension in cozero-divisor graphs ⋮ On the strong metric dimension of annihilator graphs of commutative rings ⋮ On graphs with same metric and upper dimension ⋮ Subspace-based nonzero component graph of a finite dimensional vector space

Cites Work

• The strong metric dimension of graphs and digraphs
• The total graph of a commutative ring
• Coloring of commutative rings
• The zero-divisor graph of a commutative ring
• Resolvability in graphs and the metric dimension of a graph
• Computing metric dimension of compressed zero divisor graphs associated to rings
• Zero-divisor graphs, von Neumann regular rings, and Boolean algebras.
• On the zero-divisor graph of a commutative ring
• RECOVERING RINGS FROM ZERO-DIVISOR GRAPHS
• Locating sets and numbers of graphs associated to commutative rings
• A Zero Divisor Graph Determined by Equivalence Classes of Zero Divisors
• Unit Graphs Associated with Rings
• Cut Vertices and Degree One Vertices of Zero-Divisor Graphs
• On the Metric Dimension of Cartesian Products of Graphs
• An Ideal-Based Zero-Divisor Graph of a Commutative Ring
• A ZERO-DIVISOR GRAPH FOR MODULES WITH RESPECT TO THEIR (FIRST) DUAL
• THE JACOBSON GRAPH OF COMMUTATIVE RINGS
• Annihilating-ideal graphs of commutative rings
• Upper dimension and bases of zero-divisor graphs of commutative rings
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