Results 41 to 50 of about 22,588 (272)
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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On the edge metric dimension and Wiener index of the blow up of graphs
, 2021 Let $G=(V,E)$ be a connected graph. The distance between an edge $e=xy$ and a vertex $v$ is defined as $\T{d}(e,v)=\T{min}\{\T{d}(x,v),\T{d}(y,v)\}.$ A nonempty set $S \subseteq V(G)$ is an edge metric generator for $G$ if for any two distinct edges ...
Afkhami, Mojgan
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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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Metric and Edge Metric Dimension of Zigzag Edge Coronoid Fused with Starphene
, 2021 15 pages, 2 ...
Sharma, Sunny Kumar +3 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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Computation of Edge Resolvability of Benzenoid Tripod Structure
Journal of Mathematics, 2021 In chemistry, graphs are commonly used to show the structure of chemical compounds, with nodes and edges representing the atom and bond types, respectively.
Ali Ahmad +4 more
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The local edge metric dimension of graph
Journal of Physics: Conference Series, 2020 Abstract In this paper, we introduce a new notion of graph theory study, namely a local edge metric dimension. It is a natural extension of metric dimension concept. dG (e,v) = min{d(x,v),d(y,v)} is the distance between the vertex v and the edge xy in graph G. A non empty set
R Adawiyah +5 more
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Extending the metric dimension to graphs with missing edges
Theoretical Computer Science, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sabina Zejnilovic +3 more
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Metric dimension and pattern avoidance in graphs
, 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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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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