Name
Abstract | ||
|---|---|---|
A vertex x in a connected graph G = (V, E) 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. The resolving neighborhood for the pair {u, v} is defined as R{u, v} = {x is an element of V : d(u, x) not equal d(v, x)}. A real valued function f : V -> [0, 1] is a resolving function (RF) of G if f(R{u, v}) >= 1 for any two distinct vertices u, v is an element of V. The weight of f is defined by | f| = f(V) = Sigma(u is an element of V) f(v). The fractional metric dimension dim(f) (G) is defined by dimf (G) = min{|f| : f is a resolving function of G}. In this paper, we characterize graphs G for which dim(f) (G) = |V (G)|/2. We also present several results on fractional metric dimension of Cartesian product of two connected graphs. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1142/S1793830913500377 | DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS |
Keywords | Field | DocType |
Metric dimension, fractional metric dimension, resolving set, resolving function, Cartesian product | Discrete mathematics,Graph,Combinatorics,Vertex (geometry),Cartesian product,Connectivity,Real-valued function,Mathematics,Metric dimension,Resolving set | Journal |
Volume | Issue | ISSN |
5 | 4 | 1793-8309 |
Citations | PageRank | References |
5 | 0.59 | 4 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Subramanian Arumugam | 1 | 233 | 23.23 |
| Varughese Mathew | 2 | 11 | 1.64 |
| Jian Shen | 3 | 92 | 14.67 |