- Title
- The fractional metric dimension of graphs
- Creator
- Arumugam, S.; Mathew, Varughese
- Relation
- Discrete Mathematics Vol. 312, Issue 9, p. 1584-1590
- Publisher Link
- http://dx.doi.org/10.1016/j.dam.2014.01.006
- Publisher
- Elsevier
- Resource Type
- journal article
- Date
- 2012
- Description
- 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 resolving set for G if every pair of vertices is resolved by some vertex of S. The smallest cardinality of a resolving set for G, denoted by dim(G), is called the metric dimension of G. For the pair {u,v} of vertices of G the collection of all vertices which resolve the pair {u,v} is denoted by R{u,v} and is called the resolving neighbourhood of the pair {u,v}. A real valued function g:V(G)→[0,1] is a resolving function of G if g(R{u,v})≥1 for any two distinct vertices u,v∈V(G)u. The fractional metric dimension of G is defined as dimf(G)=min{|g|:g is a minimal resolving function of G}, where |g|=∑v∈Vg(v). In this paper we study this parameter.
- Subject
- metric dimension; resolving set; basis; resolving function; fractional metric dimension
- Identifier
- http://hdl.handle.net/1959.13/1319004
- Identifier
- uon:23752
- Identifier
- ISSN:0012-365X
- Language
- eng
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