Results 21 to 30 of about 691,381 (299)
Graphs with mixed metric dimension three and related algorithms
AIMS Mathematics, 2023 Let $ G = (V, E) $ be a simple connected graph. A vertex $ x\in V(G) $ resolves the elements $ u, v\in E(G)\cup V(G) $ if $ d_G(x, u)\neq d_G(x, v) $.
Dalal Awadh Alrowaili +3 more
doaj +1 more source
Computing the Mixed Metric Dimension of a Generalized Petersen Graph P(n, 2)
Frontiers in Physics, 2020 Let Γ = (V, E) be a connected graph. A vertex i ∈ V recognizes two elements (vertices or edges) j, k ∈ E ∩ V, if dΓ(i, j) ≠ dΓ(i, k). A set S of vertices in a connected graph Γ is a mixed metric generator for Γ if every two distinct elements (vertices or
Hassan Raza, Ying Ji
doaj +1 more source
Graphs with the edge metric dimension smaller than the metric dimension [PDF]
Applied Mathematics and Computation, 2021 11 ...
Knor, Martin +4 more
openaire +3 more sources
Study of Convexo-Symmetric Networks via Fractional Dimensions
IEEE Access, 2022 For having an in-depth study and analysis of various network’s structural properties such as interconnection, extensibility, availability, centralization, vulnerability and reliability, we require distance based graph theoretic parameters ...
Muhammad Kamran Aslam +3 more
doaj +1 more source
On metric dimensions of hypercubes
Ars Mathematica Contemporanea, 2022 The metric (resp. edge metric or mixed metric) dimension of a graph $G$, is the cardinality of the smallest ordered set of vertices that uniquely recognizes all the pairs of distinct vertices (resp. edges, or vertices and edges) of $G$ by using a vector of distances to this set. In this note we show two unexpected results on hypercube graphs. First, we
Kelenc, Aleksander +3 more
openaire +4 more sources
Metric dimension and edge metric dimension of unicyclic graphs
, 2021 The metric (resp. edge metric) dimension of a simple connected graph $G$, denoted by dim$(G)$ (resp. edim$(G)$), is the cardinality of a smallest vertex subset $S\subseteq V(G)$ for which every two distinct vertices (resp. edges) in $G$ have distinct distances to a vertex of $S$.
Zhu, Enqiang +2 more
openaire +2 more sources
Contemporary Mathematics and Applications (ConMathA), 2020 Adjacency metric dimension and local adjacency metric dimension are the development of metric dimension. The purpose of this research is to determine the adjacency metric dimension of corona graph between any connected graph G and non-trivial graph H ...
Virdina Rahmayanti +2 more
doaj +1 more source
Note on Metric Dimension [PDF]
Proceedings of the American Mathematical Society, 1970 The metric dimension of a compact metric space is defined here as the order of growth of the exponential metric entropy of the space. The metric dimension depends on the metric, but is always bounded below by the topological dimension. Moreover, there is always an equivalent metric in which the metric and topological dimensions agree.
openaire +2 more sources
Bounds of Fractional Metric Dimension and Applications with Grid-Related Networks
Mathematics, 2021 Metric dimension of networks is a distance based parameter that is used to rectify the distance related problems in robotics, navigation and chemical strata. The fractional metric dimension is the latest developed weighted version of metric dimension and
Ali H. Alkhaldi +3 more
doaj +1 more source