Results 11 to 20 of about 669,922 (254)

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

PLoS ONE, 2023
The concept of metric dimension has many applications, including optimizing sensor placement in networks and identifying influential persons in social networks, which aids in effective resource allocation and focused interventions; finding the source of ...
Liu Liqin, Khurram Shahzad, Abdul Rauf, Fairouz Tchier, Adnan Aslam   +4 more
doaj   +4 more sources

On Adjacency Metric Dimension of Some Families of Graph [PDF]

Journal of Function Spaces, 2022
Metric dimension of a graph is a well-studied concept. Recently, adjacency metric dimension of graph has been introduced. A set Qa⊂VG is considered to be an adjacency metric generator for G if u1,u2∈V\Qa (supposing each pair); there must exist a vertex q∈
Ali N. A. Koam, Ali Ahmad, Muhammad Azeem, Adnan Khalil, Muhammad Faisal Nadeem   +4 more
doaj   +2 more sources

Metric Dimension Threshold of Graphs [PDF]

Journal of Mathematics, 2022
Let G be a connected graph. A subset S of vertices of G is said to be a resolving set of G, if for any two vertices u and v of G there is at least a member w of S such that du,w≠dv,w.
Meysam Korivand, Kazem Khashyarmanesh, Mostafa Tavakoli   +2 more
doaj   +2 more sources

Optimizing emergency response services in urban areas through the fault-tolerant metric dimension of hexagonal nanosheet [PDF]

Scientific Reports
In this work, we find the fault-tolerant metric dimension of a hexagonal nanosheet. This concept ensures robust identity of vertices inside a graph, even in situations in which a few resolving vertices fail.
Yaoyao Tu, Sikander Ali, Muhammad Azeem, Misbah Arshad, Ghulam Haidar, Hamdy Khamees Thabet   +5 more
doaj   +2 more sources

The dominant metric dimension of graphs [PDF]

Heliyon, 2020
The G be a connected graph with vertex set V(G) and edge set E(G). A subset S⊆V(G) is called a dominating set of G if for every vertex x in V(G)∖S, there exists at least one vertex u in S such that x is adjacent to u.
Liliek Susilowati, Imroatus Sa'adah, Ratna Zaidatul Fauziyyah, Ahmad Erfanian, Slamin   +4 more
doaj   +2 more sources

Metric dimension of star fan graph [PDF]

Scientific Reports
Every node in a network is said to be resolved if it can be uniquely identified by a vector of distances to a specific set of nodes. The metric dimension is equivalent to the least possible cardinal number of a resolving set.
S. Prabhu, D. Sagaya Rani Jeba, Sudeep Stephen   +2 more
doaj   +2 more sources

Computation of mixed resolvability for a circular ladder and its unbounded nature. [PDF]

PLoS ONE
Let Γ = Γ(V ,E) be a simple, planar, connected, and undirected graph. The article primarily concentrates on a category of planar graphs, detailing the explicit identification of each member within this graph family. Within the domain of graph theory, the
Sunny Kumar Sharma, Vijay Kumar Bhat, Muhammad Azeem, Manikonda Gayathri, Bandar Almohsen   +4 more
doaj   +2 more sources

Metric dimension and edge metric dimension of windmill graphs

AIMS Mathematics, 2021
Graph invariants provide an amazing tool to analyze the abstract structures of graphs. Metric dimension and edge metric dimension as graph invariants have numerous applications, among them are robot navigation, pharmaceutical chemistry, etc.
Pradeep Singh, Sahil Sharma, Sunny Kumar Sharma, Vijay Kumar Bhat   +3 more
doaj   +1 more source

Graphs of Neighborhood Metric Dimension Two

Journal of Mathematical and Fundamental Sciences, 2021
A subset  of vertices of a simple connected graph is a neighborhood set (n-set) of  G if G is the union of subgraphs of G induced by the closed neighbors of elements in S. Further, a set S is a resolving set of G if for each pair of distinct vertices x,y
Badekara Sooryanarayana, Suma Agani Shanmukha   +1 more
doaj   +1 more source

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
doaj   +1 more source