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 …

The base size of a permutation group, and the metric dimension of a graph, are two of a
number of related parameters of groups, graphs, coherent configurations and association …

Department of Mathematics and Statistics The University of Melbourne Melbourne comma
Australia woodd at unimelb period edu period au Submitted:.. Jul 31 comma 2008 …

The metric dimension of a graph is the smallest number of nodes required to identify all
other nodes uniquely based on shortest path distances. Applications of metric dimension …

A vertex x in a digraph D is said to resolve a pair u, v of vertices of D if the distance from u to
x does not equal the distance from v to x. A set S of vertices of D is a resolving set for D if …

Metric dimension is a distance based parameter which is used to determine the locations of
machines (or robots) with respect to minimum consumption of time, shortest distance among …

In this paper we consider two similar optimization problems on graphs: the strong metric
dimension problem and the problem of determining minimal doubly resolving sets. We prove …

For an ordered set W={w1, w2,…, wk} of vertices and a vertex v in a connected graph G, the
code of v with respect to W is the k‐vector cW (v)=(d (v, w1), d (v, w2),…, d (v, wk)), where d …

A vertex x in a connected graph G is said to resolve a pair {u, v} of vertices of G if the
distance from u to x is not equal to the distance from v to x. A set S of vertices of G is a …

Arumugam and Mathew [Discret. Math. 2012, 312, 1584–1590] introduced the notion of
fractional metric dimension of a connected graph. In this paper, a combinatorial technique is …