Results 11 to 20 of about 2,320,114 (270)

Edge Metric and Fault-Tolerant Edge Metric Dimension of Hollow Coronoid [PDF]

Mathematics, 2021
Geometric arrangements of hexagons into six sides of benzenoids are known as coronoid systems. They are organic chemical structures by definition. Hollow coronoids are divided into two types: primitive and catacondensed coronoids.
Ali N. A. Koam, Ali Ahmad, Muhammad Ibrahim, Muhammad Azeem   +3 more
doaj   +5 more sources

Asymptotic Behavior of the Edge Metric Dimension of the Random Graph [PDF]

Discussiones Mathematicae Graph Theory, 2021
Given a simple connected graph G(V,E), the edge metric dimension, denoted edim(G), is the least size of a set S ⊆ V that distinguishes every pair of edges of G, in the sense that the edges have pairwise different tuples of distances to the vertices of S.
Zubrilina Nina
doaj   +3 more sources

Identifying the Exact Value of the Metric Dimension and Edge Dimension of Unicyclic Graphs

Mathematics, 2022
Given a simple connected graph G, the metric dimension dim(G) (and edge metric dimension edim(G)) is defined as the cardinality of a smallest vertex subset S⊆V(G) for which every two distinct vertices (and edges) in G have distinct distances to a vertex ...
Enqiang Zhu, Shaoxiang Peng, Chanjuan Liu   +2 more
doaj   +6 more sources

Classes of Planar Graphs with Constant Edge Metric Dimension [PDF]

Complexity, 2021
The number of edges in a shortest walk (without repetition of vertices) from one vertex to another vertex of a connected graph G is known as the distance between them.
Changcheng Wei, Muhammad Salman, Syed Shahzaib, Masood Ur Rehman, Juanyan Fang   +4 more
doaj   +3 more sources

The K-Size Edge Metric Dimension of Graphs

Journal of Mathematics, 2020
In this paper, a new concept k-size edge resolving set for a connected graph G in the context of resolvability of graphs is defined. Some properties and realizable results on k-size edge resolvability of graphs are studied.
Tanveer Iqbal, Muhammad Naeem Azhar, Syed Ahtsham Ul Haq Bokhary   +2 more
doaj   +2 more sources

The dominant edge metric dimension of graphs

Electronic Journal of Graph Theory and Applications, 2023
For an ordered subset S = {v1, …, vk} of vertices in a connected graph G and an edge e′ of G, the edge metric S-representation of e′=ab is the vector rGe(e′|S)=(dG(e′,v1),…,dG(e′,vk)) , where dG(e′,vi)=min{dG(a, vi),dG(b, vi)}.
Mostafa Tavakoli, Meysam Korivand, Ahmad Erfanian, Gholamreza Abrishami, Edy Tri Baskoro   +4 more
doaj   +2 more sources

On the Edge Metric Dimension of Certain Polyphenyl Chains

Journal of Chemistry, 2021
The most productive application of graph theory in chemistry is the representation of molecules by the graphs, where vertices and edges of graphs are the atoms and valence bonds between a pair of atoms, respectively.
Muhammad Ahsan, Zohaib Zahid, Dalal Alrowaili, Aiyared Iampan, Imran Siddique, Sohail Zafar   +5 more
doaj   +2 more sources

Edge Metric Dimension of Some Classes of Toeplitz Networks

Journal of Mathematics, 2021
Toeplitz networks are used as interconnection networks due to their smaller diameter, symmetry, simpler routing, high connectivity, and reliability.
Dalal Alrowaili, Zohaib Zahid, Muhammad Ahsan, Sohail Zafar, Imran Siddique   +4 more
doaj   +2 more sources

On Some families of Path-related graphs with their edge metric dimension

Examples and Counterexamples
Locating the origin of diffusion in complex networks is an interesting but challenging task. It is crucial for anticipating and constraining the epidemic risks. Source localization has been considered under many feasible models.
Lianglin Li, Shu Bao, Hassan Raza
doaj   +2 more sources

Bi-Edge Metric Dimension of Graphs [PDF]

International Journal of Computing Science and Applied Mathematics
Given a connected G = (V(G),E(G)) graph. The main problem in graph metric dimensions is calculating the metric dimensions and their characterization.
Rinurwati Rinurwati, Fadillah Dian Maharani   +1 more
openaire   +2 more sources