Results 11 to 20 of about 25,129 (234)
Computation of mixed resolvability for a circular ladder and its unbounded nature. [PDF]
PLoS ONELet Γ = Γ(V ,E) be a simple, planar, connected, and undirected graph. The article primarily concentrates on a category of planar graphs, detailing the explicit identification of each member within this graph family. Within the domain of graph theory, the
Sunny Kumar Sharma +4 more
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Computing Fault-Tolerant Metric Dimension of Connected Graphs [PDF]
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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Some new general lower bounds for mixed metric dimension of graphs [PDF]
Filomat, 2021 A vertex w ? V resolves two elements x, y ? V ? E if d(w,x) ? d(w,y). The mixed resolving set is a set of vertices S, S ? V if any two elements of E ? V are resolved by some element of S. The minimum cardinality of a mixed resolving set is called the mixed metric dimension of a graph G.
Milivojević-Danas, Milica +3 more
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On mixed metric dimension in subdivision, middle, and total graphs [PDF]
Quaestiones Mathematicae, 2023 Let $G$ be a graph and let $S(G)$, $M(G)$, and $T(G)$ be the subdivision, the middle, and the total graph of $G$, respectively. Let ${\rm dim}(G)$, ${\rm edim}(G)$, and ${\rm mdim}(G)$ be the metric dimension, the edge metric dimension, and the mixed metric dimension of $G$, respectively.
Ali Ghalavand +3 more
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On mixed metric dimension of crystal cubic carbon structure
Journal of Mathematical Chemistry, 2023 Abstract Chemical graph theory is a branch of mathematical chemistry which applies classic graph theory to chemical phenomena and entities. Graphs are extensively used in chemistry to recognise the structures of chemical compounds, with the vertices and edges denoting atoms and bonds respectively.
Vijay Kumar Bhat +2 more
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Graphs whose mixed metric dimension is equal to their order
Computational and Applied Mathematics, 2023 The mixed metric dimension ${\rm mdim}(G)$ of a graph $G$ is the cardinality of a smallest set of vertices that (metrically) resolves each pair of elements from $V(G)\cup E(G)$. We say that $G$ is a max-mdim graph if ${\rm mdim}(G) = n(G)$. It is proved that a max-mdim graph $G$ with $n(G)\ge 7$ contains a vertex of degree at least $5$.
Sandi Klavžar +2 more
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On Resolvability- and Domination-Related Parameters of Complete Multipartite Graphs [PDF]
Mathematics, 2022 Graphs of order n with fault-tolerant metric dimension n have recently been characterized.This paper points out an error in the proof of this characterization. We show that the complete multipartite graphs also have the fault-tolerant metric dimension n,
Sakander Hayat, Asad Khan, Yubin Zhong
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A Comparative Study of Three Resolving Parameters of Graphs [PDF]
Complexity, 2021 Graph theory is one of those subjects that is a vital part of the digital world. It is used to monitor the movement of robots on a network, to debug computer networks, to develop algorithms, and to analyze the structural properties of chemical structures,
Hafiz Muhammad Ikhlaq +2 more
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Computing dominant metric dimensions of certain connected networks [PDF]
HeliyonIn the studies of the connected networks, metric dimension being a distance-based parameter got much more attention of the researches due to its wide range of applications in different areas of chemistry and computer science. At present its various types
Imtiaz Ali, Muhammad Javaid, Yilun Shang
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Honeycomb Rhombic Torus Vertex-Edge Based Resolvability Parameters and Its Application in Robot Navigation [PDF]
IEEE AccessIn the aircraft sector, honeycomb composite materials are frequently employed. Recent research has demonstrated the benefits of honeycomb structures in applications involving nanohole arrays in anodized alumina, micro-porous arrays in polymer thin films,
Sidra Bukhari +3 more
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