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- W2059749917 abstract "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). 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." @default.
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- W2059749917 date "2012-05-01" @default.
- W2059749917 modified "2023-10-16" @default.
- W2059749917 title "The fractional metric dimension of graphs" @default.
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- W2059749917 doi "https://doi.org/10.1016/j.disc.2011.05.039" @default.
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