Results 41 to 50 of about 253,596 (293)
European Journal of Pure and Applied MathematicsWhen there is a difference in the distance between two vertices in a simple linked graph, then a vertex $x$ resolves both $u$ and $v$. If at least one vertex in $S$ distinguishes each pair of distinct vertices in $G$, then a set $S$ of vertices in $G$ is referred to as a resolving set.
Waseem Abbas +4 more
openalex +3 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.
Robiatul Adawiyah +4 more
openalex +2 more sources
Bi-Edge Metric Dimension of Graphs
International Journal of Computing Science and Applied MathematicsRinurwati Rinurwati +1 more
openalex +3 more sources
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
Fault-tolerant edge metric dimension of certain families of graphs
AIMS Mathematics, 2021 Let $W_E=\{w_1,w_2, \ldots,w_k\}$ be an ordered set of vertices of graph $G$ and let $e$ be an edge of $G$. Suppose $d(x,e)$ denotes distance between edge $e$ and vertex $x$ of $G$, defined as $d(e,x) = d(x,e) = \min \{d(x,a),d(x,b)\}$, where $e=ab$.
Xiaogang Liu +3 more
doaj +1 more source
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
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
Remarks on the Vertex and the Edge Metric Dimension of 2-Connected Graphs
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 +1 more source