Results 51 to 60 of about 2,452,302 (284)
On Mixed Metric Dimension of Rotationally Symmetric Graphs
IEEE Access, 2020 A vertex u ∈ V(G) resolves (distinguish or recognize) two elements (vertices or edges) v, w ∈ E(G)UV(G) if dG(u, v) ≠ dG(u, w) . A subset Lm of vertices in a connected graph G is called a mixed metric generator for G if every two ...
Hassan Raza, Jia-Bao Liu, Shaojian Qu
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Fault-tolerant edge metric dimension of certain families of graphs
AIMS Mathematics, 2021 Let $W_E=\{w_1,w_2, \ldots,w_k\}$ be an ordered set of vertices of graph $G$ and let $e$ be an edge of $G$. Suppose $d(x,e)$ denotes distance between edge $e$ and vertex $x$ of $G$, defined as $d(e,x) = d(x,e) = \min \{d(x,a),d(x,b)\}$, where $e=ab$.
Xiao-Gang Liu +3 more
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On Mixed Metric Dimension of Some Path Related Graphs
IEEE Access, 2020 A vertex $k\in V_{G}$ determined two elements (vertices or edges) $\ell,m \in V_{G}\cup E_{G}$ , if $d_{G}(k,\ell)\neq d_{G}(k,m)$ . A set $R_ {\text {m}}$ of vertices in a graph $G$ is a mixed metric generator for $G$ , if two distinct elements
Hassan Raza, Ying Ji, Shaojian Qu
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Metric dimension and edge metric dimension of unicyclic graphs
, 2021 The metric (resp. edge metric) dimension of a simple connected graph $G$, denoted by dim$(G)$ (resp. edim$(G)$), is the cardinality of a smallest vertex subset $S\subseteq V(G)$ for which every two distinct vertices (resp. edges) in $G$ have distinct distances to a vertex of $S$.
Zhu, Enqiang +2 more
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Uniquely identifying the edges of a graph: The edge metric dimension [PDF]
Discrete Applied Mathematics, 2016 Let $G=(V,E)$ be a connected graph, let $v\in V$ be a vertex and let $e=uw\in E$ be an edge. The distance between the vertex $v$ and the edge $e$ is given by $d_G(e,v)=\min\{d_G(u,v),d_G(w,v)\}$.
Aleksander Kelenc +2 more
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Patched Network and Its Vertex-Edge Metric-Based Dimension
IEEE Access, 2023 The p-type networks are designed with the help of CVNET at topo group Cluj and also given support by nano studio. Such networks develop new p-type surfaces and also represent the decorations of the surfaces.
Sidra Bukhari +3 more
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Bounds on metric dimensions of graphs with edge disjoint cycles [PDF]
Applied Mathematics and Computation, 2021 In a graph G, cardinality of the smallest ordered set of vertices that distinguishes every element of V (G) is the (vertex) metric dimension of G. Similarly, the cardinality of such a set is the edge metric dimension of G, if it distinguishes E(G). In this paper these invariants are considered first for unicyclic graphs, and it is shown that the vertex
Jelena Sedlar, Riste Skrekovski
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Computing the Mixed Metric Dimension of a Generalized Petersen Graph P(n, 2)
Frontiers in Physics, 2020 Let Γ = (V, E) be a connected graph. A vertex i ∈ V recognizes two elements (vertices or edges) j, k ∈ E ∩ V, if dΓ(i, j) ≠ dΓ(i, k). A set S of vertices in a connected graph Γ is a mixed metric generator for Γ if every two distinct elements (vertices or
Hassan Raza, Ying Ji
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PROPERTIES OF CERTAIN CONNECTED GRAPHS RELATED TO THEIR EDGE METRIC DIMENSION [PDF]
, 2022 Metric dimension, resolving sets and edge metric dimension are very important invariants for the resolvability of graphs that have been studied and investigated intensively in the literature over the last decades.
Bisharat, Sanabel Mahmoud Y.
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On Resolvability Parameters of Some Wheel-Related Graphs
Journal of Chemistry, 2019 Let G=V,E be a simple connected graph, w∈V be a vertex, and e=uv∈E be an edge. The distance between the vertex w and edge e is given by de,w=mindw,u,dw,v, A vertex w distinguishes two edges e1, e2∈E if dw,e1≠dw,e2.
Bin Yang +3 more
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