Results 41 to 50 of about 429,051 (306)
Edge and mixed metric dimension of Johnson graphs [PDF]
In this paper, both edge and mixed metric dimensions of Johnson graphs $J_{n,k}$ are considered. A new tight lower bound for $β_E(J_{n,k})$ based on hitting sets has been obtained. Using this bound, exact values for $β_E(J_{n,2})$ and $β_M(J_{n,2})$ have been derived, and it is proved that $β_E(J_{n,2}) = β_M(J_{n,2})$.
Jozef Kratica +3 more
openalex +3 more sources
On graphs with the maximum edge metric dimension
Discrete Applied Mathematics, 2019 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Enqiang Zhu +3 more
openaire +2 more sources
Edge Metric Dimension of Silicate Networks [PDF]
Metric dimension is an essential parameter in graph theory that aids in addressing issues pertaining to information retrieval, localization, network design, and chemistry through the identification of the least possible number of elements necessary to identify the distances between vertices in a graph uniquely. A variant of metric dimension, called the
S. Prabhu, T. Jenifer Janany
openalex +3 more sources
The Metric Dimension of Graph with Pendant Edges [PDF]
, 2008 Summary: For an ordered set \(W = \{w_1,w_2,\dots,w_k\}\) of vertices and a vertex \(v\) in a connected graph \(G\), the representation of \(v\) with respect to \(W\) is the ordered \(k\)-tuple \(r(vlW) = (d(v, w_1),d(v,w_1),\dots,d(v,w_k))\) where \(d(x,y)\) represents the distance between tKe vertices \(x\) and \(y\).
Hazrul Iswadi +3 more
openalex +2 more sources
Edge Metric Dimension on Some Families of Tree
Journal of Physics: Conference Series, 2019 Metric Dimension as a graph invariant has various applications in real life. One of the metric dimension application is for the navigation system in transportation. In this Paper, we continue to develop the study of edge metric dimension. Let G = (V, E) be a connected graph with v ∈ V and e = uw ∈ E.
R. Adawiyah +4 more
openaire +2 more sources
Bi-Edge Metric Dimension of Graphs
International Journal of Computing Science and Applied MathematicsRinurwati Rinurwati +1 more
openaire +2 more sources
On Metric Dimension of Edge Comb Product of Symmetric Graphs
Jurnal Matematika UNANDConsider a finite graph G that is simple, undirected, and connected. Let W be an ordered set of vertices with |W| = k. The representation of a vertex v is defined as an ordered k-tuple that consists of the distances from vertex v to each vertex in W. The
Tita Khalis Maryati +2 more
doaj +2 more sources
Edge Metric Dimension of Honeycomb and Hexagonal Networks for IoT
Computers Materials & Continua, 2022 : Wireless Sensor Network (WSN) is considered to be one of the fundamental technologies employed in the Internet of things (IoT); hence, enabling diverse applications for carrying out real-time observations. Robot navigation in such networks was the main
S. Abbas +4 more
semanticscholar +1 more source
Vertex and edge metric dimensions of cacti
Discrete applied mathematics, 2022 In a graph G, a vertex (resp. an edge) metric generator is a set of vertices S such that any pair of vertices (resp. edges) from G is distinguished by at least one vertex from S. The cardinality of a smallest vertex (resp. edge) metric generator is the vertex (resp. edge) metric dimension of G. In [?] we determined the vertex (resp.
Jelena Sedlar, Riste Škrekovski
openaire +5 more sources
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