Metric and fault-tolerant metric dimension for GeSbTe superlattice chemical structure. [PDF]
PLoS ONE, 2023 The concept of metric dimension has many applications, including optimizing sensor placement in networks and identifying influential persons in social networks, which aids in effective resource allocation and focused interventions; finding the source of ...
Liu Liqin +4 more
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Fault-Tolerant Metric Dimension of Circulant Graphs [PDF]
Mathematics, 2022 Let G be a connected graph with vertex set V(G) and d(u,v) be the distance between the vertices u and v. A set of vertices S={s1,s2,…,sk}⊂V(G) is called a resolving set for G if, for any two distinct vertices u,v∈V(G), there is a vertex si∈S such that d ...
Laxman Saha +4 more
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Metric and Fault-Tolerant Metric Dimension of Hollow Coronoid [PDF]
IEEE Access, 2021 Coronoid systems actually arrangements of hexagons into six sides of benzenoids. By nature, it is an organic chemical structure. Hollow coronoids are primitive and catacondensed coronoids. It is also known as polycyclic conjugated hydrocarbons.
Ali N. A. Koam +3 more
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Fault-tolerance in metric dimension of boron nanotubes lattices [PDF]
Frontiers in Computational Neuroscience, 2023 The concept of resolving set and metric basis has been very successful because of multi-purpose applications both in computer and mathematical sciences.
Zafar Hussain, Muhammad Mobeen Munir
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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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Computing Fault-Tolerant Metric Dimension of Connected Graphs
Journal of Mathematics, 2022 For a connected graph, the concept of metric dimension contributes an important role in computer networking and in the formation of chemical structures.
Uzma Ahmad +3 more
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Fault-Tolerant Metric Dimension of Interconnection Networks [PDF]
IEEE Access, 2020 A fixed interconnection parallel architecture is characterized by a graph, with vertices corresponding to processing nodes and edges representing communication links.
Sakander Hayat +4 more
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Edge Metric and Fault-Tolerant Edge Metric Dimension of Hollow Coronoid [PDF]
Mathematics, 2021 Geometric arrangements of hexagons into six sides of benzenoids are known as coronoid systems. They are organic chemical structures by definition. Hollow coronoids are divided into two types: primitive and catacondensed coronoids.
Ali N. A. Koam +3 more
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Twin vertices in fault-tolerant metric sets and fault-tolerant metric dimension of multistage interconnection networks [PDF]
Applied Mathematics and Computation, 2022 A set of vertices $S\subseteq V(G)$ is a basis or resolving set of a graph $G$ if for each $x,y\in V(G)$ there is a vertex $u\in S$ such that $d(x,u)\neq d(y,u)$. A basis $S$ is a fault-tolerant basis if $S\setminus \{x\}$ is a basis for every $x \in S$.
S Prabhu +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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