Results 11 to 20 of about 3,384,887 (243)
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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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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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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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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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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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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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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On mixed metric dimension in subdivision, middle, and total graphs [PDF]
, 2022 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 ...
Ghalavand, Ali +3 more
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