Results 11 to 20 of about 2,452,302 (284)
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 +3 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 +4 more
doaj +4 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 +4 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 +4 more
doaj +3 more sources
Remarks on the Vertex and the Edge Metric Dimension of 2-Connected Graphs [PDF]
Mathematics, 2022 The vertex (respectively edge) metric dimension of a graph G is the size of a smallest vertex set in G, which distinguishes all pairs of vertices (respectively edges) in G, and it is denoted by dim(G) (respectively edim(G)). The upper bounds dim(G)≤2c(G)−
Martin Knor +2 more
doaj +4 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 +5 more
doaj +3 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 +4 more
doaj +3 more sources
Computing Edge Metric Dimension of One-Pentagonal Carbon Nanocone
Frontiers in Physics, 2021 Minimum resolving sets (edge or vertex) have become an integral part of molecular topology and combinatorial chemistry. Resolving sets for a specific network provide crucial information required for the identification of each item contained in the ...
Sunny Kumar Sharma +2 more
doaj +4 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 +2 more
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 +2 more
doaj +6 more sources