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[HTML][HTML] Uniquely identifying the edges of a graph: the edge metric dimension
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 …
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
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 …
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
The concept of metric dimension has many applications, including optimizing sensor
placement in networks and identifying influential persons in social networks, which aids in …
placement in networks and identifying influential persons in social networks, which aids in …
Metric dimension of maximal outerplanar graphs
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 …
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
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 …
availability conditions to ensure effective and efficient operation. As a result, several power …
On the metric dimension of infinite graphs
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 …
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
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 …
whose distances to these vertices are distinct. In this paper R-sets are used to show that …
[HTML][HTML] Metric dimension of generalized wheels
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 …
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
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 …
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
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 …
distinguishes all vertices of $ G $ using the shortest distance from this subset. This subset is …