Results 11 to 20 of about 249,139 (224)
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.
Malkesh Singh, Vijay Kumar Bhat
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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 Klavzar, Mostafa Tavakoli
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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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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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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 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 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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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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Remote Sensing, 2022 Unmanned Aerial Vehicles (UAVs) can be employed as low-altitude aerial base stations (UAV-BSs) to provide communication services for ground users (GUs).
Yi Zhou +5 more
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