Results 41 to 50 of about 238,609 (287)
On the metric dimension of Cayley graphs
AKCE International Journal of Graphs and Combinatorics, 2022 In this paper, we investigate the metric dimension, local metric dimension and edge metric dimension for some (generalized) Cayley graphs.
Afsaneh Rezaei +2 more
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Edge Metric Dimension of Honeycomb and Hexagonal Networks for IoT
Computers Materials & Continua, 2022 : Wireless Sensor Network (WSN) is considered to be one of the fundamental technologies employed in the Internet of things (IoT); hence, enabling diverse applications for carrying out real-time observations. Robot navigation in such networks was the main
S. Abbas +4 more
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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 $e=ab$.
Xiaogang 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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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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Metric dimension and pattern avoidance in graphs [PDF]
, 2018 We prove that the maximum possible number of edges in a graph of diameter $D$ and edge metric dimension $k$ is at most $(\lfloor \frac{2D}{3}\rfloor +1)^{k}+k \sum_{i = 1}^{\lceil \frac{D}{3}\rceil } (2i-1)^{k-1}$, sharpening the bound of $\binom{k}{2}+k
Jesse Geneson
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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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