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Edge Metric Dimension of Some Generalized Petersen Graphs [PDF]

Results in Mathematics, 2019
The edge metric dimension problem was recently introduced, which initiated the study of its mathematical properties. The theoretical properties of the edge metric representations and the edge metric dimension of generalized Petersen graphs $GP(n,k)$ are studied in this paper. We prove the exact formulae for $GP(n,1)$ and $GP(n, 2)$, while for the other
Aleksandar Kartelj, Vladimir Filipović, Jozef Kratica   +2 more
exaly   +3 more sources

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The edge metric dimensions of convex polytopes

Discrete Applied Mathematics
Jinfeng Liu, Changhong Lu, Jinfeng Liu
exaly   +3 more sources

Computing edge version of metric and double metric dimensions of Kayak paddle graphs

Discrete Mathematics, Algorithms and Applications, 2020
Locating the source of diffusion in complex networks is an exciting but challenging task. It is critical for preventing and controlling the epidemic risks. Source localization has been studied under many feasible models. In this paper, we discuss the localization problem in Kayak paddle graphs [Formula: see text] for [Formula: see text] and [Formula ...
Muhammad Ahmad 0003, Naeem Ameen, Zohaib Zahid, Sohail Zafar   +3 more
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Metric and edge metric dimensions of generalized Andrásfai graphs

Discrete Applied Mathematics
A W⊆V(G) is a resolving set (edge resolving set) if for every pair in V(G) (E(G)), there exists a w∈W such that they are not at the same distance from w. A cardinality which is least over all resolving set (edge resolving set) is called metric dimension (edge metric dimension) of G, coined as dim(G) (dime(G)).
S. Prabhu, K. Bharani Dharan, S. Radha, Akbar Davoodi   +3 more
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The metric dimension of graph with pendant edges

2008
Summary: For an ordered set \(W = \{w_1,w_2,\dots,w_k\}\) of vertices and a vertex \(v\) in a connected graph \(G\), the representation of \(v\) with respect to \(W\) is the ordered \(k\)-tuple \(r(vlW) = (d(v, w_1),d(v,w_1),\dots,d(v,w_k))\) where \(d(x,y)\) represents the distance between tKe vertices \(x\) and \(y\).
Iswadi, Hazrul, Baskoro, Edy Tri, Simanjuntak, Rinovia, Salman, A.N.M   +3 more
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Edge metric dimension of fullerenes

2023
Bonyabadilrm;, Parvane, Khashyarmanesh, Kazem, Tavakoli, Mostafa, Afkhami, Mojgan   +3 more
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The K-edge metric dimension of a graph

Discrete Mathematics, Algorithms and Applications
The main advantage of the edge metric basis in the detection problem is that it identifies every distinct pair of edges in a simple connected graph [Formula: see text] by placing detectors at selected vertices. However, if one detector fails, the entire system breaks down.
Nosheen Goshi, Sohail Zafar, Tabasam Rashid   +2 more
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The complement edge metric dimension of graphs

AIP Conference Proceedings, 2022
Nirmala Mega Rosyidah, null Rinurwati
openaire   +1 more source

Edge metric dimension and mixed metric dimension of planar graph

Discrete Applied Mathematics, 2022
Nanbin Cao
exaly  

Vertex and edge metric dimensions of unicyclic graphs

Discrete Applied Mathematics, 2022
Riste Škrekovski, Jelena Sedlar
exaly