Let G = (V, E) be a connected graph and d(x, y) be the distance between the vertices x and y in G. A set of vertices W resolves a graph G if every vertex is uniquely determined by its vector of distances to the vertices in W. A metric dimension of G is the minimum cardinality of a resolving set of G and is denoted by dim(G). In this paper, Cycle, Path, Harary graphs and their rooted product as well as their connectivity are studied and their metric dimension is calculated. It is proven that metric dimension of some graphs is unbounded while the other graphs are constant, having three or four dimensions in certain cases
A metric basis for a digraph G(V, A) is a set W⊂V such that for each pair of vertices u and v of V, ...
Let G be a connected graph. Given an ordered set W = {w1, . . . , wk} ⊆ V (G) and a vertex u ∈ V (G)...
Abstract: A graph G = (V, E) is a non-empty collection of vertices and edges, where V is the vertex ...
Let G = (V, E) be a connected graph and d(x, y) be the distance between the vertices x and y in G. A...
Abstract. A set of vertices S resolves a graph G if every vertex is uniquely determined by its vecto...
A set of vertices W resolves a graph G if every vertex of G is uniquely deter-mined by its vector of...
Metric dimension or location number is a generalization of affine dimension to arbitrary metric spac...
AbstractGiven a set of vertices S={v1,v2,…,vk} of a connected graph G, the metric representation of ...
A set of vertices S resolves a graph G if every vertex is uniquely determined by its vector of dista...
The distance d(va,vb) between two vertices of a simple connected graph G is the length of the shorte...
The distance d(va,vb) between two vertices of a simple connected graph G is the length of the shorte...
Let G = ( V ( G ) , E ( G ) ) be a connected graph. An ordered set W ⊂ V ( G ) i...
For an ordered set W = {w_1,w_2,...,w_k} of vertices and a vertex v in a connected graph G, the repr...
AbstractA set of vertices S resolves a graph G if every vertex is uniquely determined by its vector ...
Infinite graph; Locally finite graph; Resolving set; Metric dimension; Cartesian...
A metric basis for a digraph G(V, A) is a set W⊂V such that for each pair of vertices u and v of V, ...
Let G be a connected graph. Given an ordered set W = {w1, . . . , wk} ⊆ V (G) and a vertex u ∈ V (G)...
Abstract: A graph G = (V, E) is a non-empty collection of vertices and edges, where V is the vertex ...
Let G = (V, E) be a connected graph and d(x, y) be the distance between the vertices x and y in G. A...
Abstract. A set of vertices S resolves a graph G if every vertex is uniquely determined by its vecto...
A set of vertices W resolves a graph G if every vertex of G is uniquely deter-mined by its vector of...
Metric dimension or location number is a generalization of affine dimension to arbitrary metric spac...
AbstractGiven a set of vertices S={v1,v2,…,vk} of a connected graph G, the metric representation of ...
A set of vertices S resolves a graph G if every vertex is uniquely determined by its vector of dista...
The distance d(va,vb) between two vertices of a simple connected graph G is the length of the shorte...
The distance d(va,vb) between two vertices of a simple connected graph G is the length of the shorte...
Let G = ( V ( G ) , E ( G ) ) be a connected graph. An ordered set W ⊂ V ( G ) i...
For an ordered set W = {w_1,w_2,...,w_k} of vertices and a vertex v in a connected graph G, the repr...
AbstractA set of vertices S resolves a graph G if every vertex is uniquely determined by its vector ...
Infinite graph; Locally finite graph; Resolving set; Metric dimension; Cartesian...
A metric basis for a digraph G(V, A) is a set W⊂V such that for each pair of vertices u and v of V, ...
Let G be a connected graph. Given an ordered set W = {w1, . . . , wk} ⊆ V (G) and a vertex u ∈ V (G)...
Abstract: A graph G = (V, E) is a non-empty collection of vertices and edges, where V is the vertex ...