Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4647036 | Discrete Mathematics | 2014 | 12 Pages |
Abstract
Let G be a connected graph. A vertex w strongly resolves a pair u,v of vertices of G if there exists some shortest uâw path containing v or some shortest vâw path containing u. A set W of vertices is a strong resolving set for G if every pair of vertices of G is strongly resolved by some vertex of W. The smallest cardinality of a strong resolving set for G is called the strong metric dimension of G. It is known that the problem of computing the strong metric dimension of a graph is NP-hard. In this paper we obtain closed formulae for the strong metric dimension of several families of Cartesian products of graphs and direct products of graphs.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Juan A. RodrÃguez-Velázquez, Ismael G. Yero, Dorota Kuziak, Ortrud R. Oellermann,