منابع مشابه
The metric dimension and girth of graphs
A set $Wsubseteq V(G)$ is called a resolving set for $G$, if for each two distinct vertices $u,vin V(G)$ there exists $win W$ such that $d(u,w)neq d(v,w)$, where $d(x,y)$ is the distance between the vertices $x$ and $y$. The minimum cardinality of a resolving set for $G$ is called the metric dimension of $G$, and denoted by $dim(G)$. In this paper, it is proved that in a connected graph $...
متن کاملthe metric dimension and girth of graphs
a set $wsubseteq v(g)$ is called a resolving set for $g$, if for each two distinct vertices $u,vin v(g)$ there exists $win w$ such that $d(u,w)neq d(v,w)$, where $d(x,y)$ is the distance between the vertices $x$ and $y$. the minimum cardinality of a resolving set for $g$ is called the metric dimension of $g$, and denoted by $dim(g)$. in this paper, it is proved that in a connected graph $...
متن کاملMetric Dimension for Random Graphs
The metric dimension of a graph G is the minimum number of vertices in a subset S of the vertex set of G such that all other vertices are uniquely determined by their distances to the vertices in S. In this paper we investigate the metric dimension of the random graph G(n, p) for a wide range of probabilities p = p(n).
متن کاملMetric Dimension for Amalgamations of Graphs
A set of vertices S resolves a graph G if every vertex is uniquely determined by its vector of distances to the vertices in S. The metric dimension of G is the minimum cardinality of a resolving set of G. Let {G1, G2, . . . , Gn} be a finite collection of graphs and each Gi has a fixed vertex v0i or a fixed edge e0i called a terminal vertex or edge, respectively. The vertex-amalgamation of G1, ...
متن کاملOn the metric dimension of Grassmann graphs
The metric dimension of a graph Γ is the least number of vertices in a set with the property that the list of distances from any vertex to those in the set uniquely identifies that vertex. We consider the Grassmann graph Gq(n,k) (whose vertices are the k-subspaces of Fq, and are adjacent if they intersect in a (k− 1)-subspace) for k ≥ 2. We find an upper bound on its metric dimension, which is ...
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ژورنال
عنوان ژورنال: Opuscula Mathematica
سال: 2019
ISSN: 1232-9274
DOI: 10.7494/opmath.2019.39.3.415