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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 $5$.
Ali Ghalavand +2 more
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Longitudinal Sigma-Metric Profiling of Two Clinical Chemistry Platforms Using Peer-Group Internal Quality Control [PDF]
DiagnosticsBackground: The Six Sigma metric benchmarks analytical performance, but most reports assess one platform at one time point, merging trueness with imprecision.
Indah Meyliza +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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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, Malkesh Singh
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Extremal mixed metric dimension with respect to the cyclomatic number [PDF]
Applied Mathematics and Computation, 2021 14 pages, 3 ...
Jelena Sedlar, Riste Skrekovski
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Multiset and Mixed Metric Dimension for Starphene and Zigzag-Edge Coronoid [PDF]
Polycyclic Aromatic Compounds, 2021 Let $Γ=(V,E)$ be a simple connected graph. A vertex $a$ is said to recognize (resolve) two different elements $b_{1}$ and $b_{2}$ from $V(Γ)\cup E(Γ)$ if $d(a, b_{1})\neq d(a, b_{2}\}$. A subset of distinct ordered vertices $U_{M}\subseteq V(Γ)$ is said to be a mixed metric generator for $Γ$ if each pair of distinct elements from $V\cup E$ are ...
Jia-Bao Liu +3 more
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On Resolvability- and Domination-Related Parameters of Complete Multipartite Graphs
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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The Vertex-Edge Resolvability of Some Wheel-Related Graphs
Journal of Mathematics, 2021 A vertex w∈VH distinguishes (or resolves) two elements (edges or vertices) a,z∈VH∪EH if dw,a≠dw,z. A set Wm of vertices in a nontrivial connected graph H is said to be a mixed resolving set for H if every two different elements (edges and vertices) of H ...
Bao-Hua Xing +4 more
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The mixed metric dimension of wheel-like graphs
Journal of Physics: Conference Series, 2022 Abstract Consider the graph G = (V, E). It is a connected graph. It is a simple graph too. A node w ∈ V, then we call vertex, determined two elements of graph. There are vertices and edges of graphs. Any two vertices x, y ∈ E ∪ V if d(w, x) ≠ d(w, y), which d(w, x) and d(w, y) is the mixed distance of the element w (vertices or edges) in
null Darmaji, N Azahra
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A Comparative Study of Three Resolving Parameters of Graphs
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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