Results 11 to 20 of about 684 (218)
All metric bases and fault-tolerant metric dimension for square of grid [PDF]
Opuscula Mathematica, 2022 For a simple connected graph \(G=(V,E)\) and an ordered subset \(W = \{w_1,w_2,\ldots, w_k\}\) of \(V\), the code of a vertex \(v\in V\), denoted by \(\mathrm{code}(v)\), with respect to \(W\) is a \(k\)-tuple \((d(v,w_1),\ldots, d(v, w_k))\), where \(d ...
Laxman Saha +2 more
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Fault-tolerant metric dimension of zero-divisor graphs of commutative rings [PDF]
AKCE International Journal of Graphs and Combinatorics, 2021 Let R be a commutative ring with identity. The zero-divisor graph of R denoted by is an undirected graph where is the set of non-zero zero-divisors of R and there is an edge between the vertices z1 and z2 in if A set of vertices S resolves a graph G if ...
Sahil Sharma, Vijay Kumar Bhat
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Fault-Tolerant Metric Dimension of Cube of Paths
Journal of Physics: Conference Series, 2021 Abstract For a simple connected graph G = (V (G), E(G)), a set R ⊆ V (G) is said to be a resolving set of G if every pair of vertices of G are resolved by some vertices in R i.e., every pair of vertices of G are identified uniquely by some vertex elements in F.
Laxman Saha
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Studies of Multilevel Networks via Fault-Tolerant Metric Dimensions
IEEE Access, 2022 A subset $T$ of the vertex set of a network $G$ is called a resolving set for $G$ if each pair of vertices of $G$ have distinct representations with respect to $T$ . A resolving set $B^{\prime} $ among all the resolving sets of a network $G$
Imtiaz Ali +2 more
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Fault tolerance in para-line network topologies: theory and applications in smart systems [PDF]
Scientific ReportsThis study explores the fault-tolerant metric dimension (FTMD) of the para-line network, which is derived from the n-sunlet network, a significant category of networks created by subdividing and transforming cycle-based networks to simulate greater ...
Sanaa Ahmed Bajri +5 more
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Fault-Tolerant Metric Dimension in Carbon Networks
FoundationsIn this paper, we study the fault-tolerant metric dimension in graph theory, an important measure against failures in unique vertex identification. The metric dimension of a graph is the smallest number of vertices required to uniquely identify every ...
Kamran Azhar, Asim Nadeem, Yilun Shang
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Fault-Tolerant Metric Dimension and Applications: Zero-Divisor Graph of Upper Triangular Matrices
MathematicsGraph invariants play a crucial role in understanding the structural and combinatorial characteristics of graphs. The fault-tolerant metric dimension, as a significant graph invariant, finds applications in diverse areas such as robust network ...
Latif Abdelmalek Hanna +2 more
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FAULT-TOLERANT METRIC DIMENSION OF ANNIHILATOR GRAPHS OF COMMUTATIVE RINGS [PDF]
Journal of Algebraic SystemsLet R be a commutative ring with identity. The annihilator graph AG (R) is a simple graph with vertex set as the set of all non-zero zero-divisors of R, and two distinct vertices a and b are adjacent if and only if annR (a) ∪ annR (b) ̸= annR (a · b). We
Mohan S. Akhila, Karunakaran Manilal
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Investigating the Metric and Fault-Tolerant Dimensions in Para-Line Network Topologies
AKCE International Journal of Graphs and CombinatoricsThe resolving set (RS) and metric dimension (MD) are critical concepts used in various fields such as computer networks, robot navigation, chemical structures, communication networks, transportation, and electric circuits.
M. Faheem +5 more
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Fault-Tolerant Edge Metric Dimension of Zero-Divisor Graphs of Commutative Rings
AxiomsIn recent years, the intersection of algebraic structures and graph-theoretic concepts has developed significant interest, particularly through the study of zero-divisor graphs derived from commutative rings.
Omaima Alshanquiti +2 more
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