[HTML][HTML] Uniquely identifying the edges of a graph: the edge metric dimension

A Kelenc, N Tratnik, IG Yero - Discrete Applied Mathematics, 2018‏ - Elsevier
Abstract Let G=(V, E) be a connected graph, let v∈ V be a vertex and let e= uw∈ 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 …

[HTML][HTML] On the strong metric dimension of Cartesian and direct products of graphs

JA Rodríguez-Velázquez, IG Yero, D Kuziak… - Discrete …, 2014‏ - Elsevier
Let G be a connected graph. A vertex w strongly resolves a pair u, v of vertices of G if there
exists some shortest u− w path containing v or some shortest v− w path containing u. A set W …

Metric and fault-tolerant metric dimension for GeSbTe superlattice chemical structure

L Liqin, K Shahzad, A Rauf, F Tchier, A Aslam - Plos one, 2023‏ - journals.plos.org
The concept of metric dimension has many applications, including optimizing sensor
placement in networks and identifying influential persons in social networks, which aids in …

Metric dimension of maximal outerplanar graphs

M Claverol, A García, G Hernández… - Bulletin of the Malaysian …, 2021‏ - Springer
In this paper, we study the metric dimension problem in maximal outerplanar graphs.
Concretely, if β (G) β (G) denotes the metric dimension of a maximal outerplanar graph G of …

Resolving-power domination number of probabilistic neural networks

S Prabhu, S Deepa, M Arulperumjothi… - Journal of Intelligent …, 2022‏ - content.iospress.com
Power utilities must track their power networks to respond to changing demand and
availability conditions to ensure effective and efficient operation. As a result, several power …

On the metric dimension of infinite graphs

J Cáceres, C Hernando, M Mora, IM Pelayo… - Electronic Notes in …, 2009‏ - Elsevier
A set of vertices S resolves a connected graph G if every vertex is uniquely determined by its
vector of distances to the vertices in S. The metric dimension of a graph G is the minimum …

[PDF][PDF] R-sets and metric dimension of necklace graphs

I Tomescu, M Imran - Applied Mathematics & Information …, 2015‏ - naturalspublishing.com
The R-set relative to a pair of distinct vertices of a connected graph G is the set of vertices
whose distances to these vertices are distinct. In this paper R-sets are used to show that …

[HTML][HTML] Metric dimension of generalized wheels

B Sooryanarayana, S Kunikullaya… - Arab Journal of …, 2019‏ - Elsevier
In a graph G, a vertex w∈ V (G) resolves a pair of vertices u, v∈ V (G) if d (u, w)≠ d (v, w). A
resolving set of G is a set of vertices S such that every pair of distinct vertices in V (G) is …

Metric dimensions of bicyclic graphs with potential applications in Supply Chain Logistics

M Wang, G Haidar, F Yousafzai, MUI Khan… - arxiv preprint arxiv …, 2024‏ - arxiv.org
Metric dimensions and metric basis are graph invariants studied for their use in locating and
indexing nodes in a graph. It was recently established that for bicyclic graph of type-III …

Fault Tolerant Metric Dimensions of Leafless Cacti Graphs with Application in Supply Chain Management

T Asif, G Haidar, F Yousafzai, MUI Khan… - arxiv preprint arxiv …, 2024‏ - arxiv.org
A resolving set for a simple graph $ G $ is a subset of vertex set of $ G $ such that it
distinguishes all vertices of $ G $ using the shortest distance from this subset. This subset is …