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On the k-Metric Dimension of Graphs

Publication Type : Journal Article

Publisher : Journal of Mathematics and Computational Science

Source : Journal of Mathematics and Computational Science, scik, Volume 4, Issue 5, Number 5, p.861–878 (2014)

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Campus : Bengaluru

School : School of Engineering

Department : Mathematics

Year : 2014

Abstract : Let G(V,E) be a connected graph. A subset S of V is said to be k-resolving set of G, if for every pair of distinct vertices u, v ∈/ S, there exists a vertex w ∈ S such that |d(u,w)−d(v,w)| ≥ k, for some k ∈ Z +. Among all k-resolving sets of G, the set having minimum cardinality is called a k-metric basis of G and its cardinality is called the k-metric dimension of G and is denoted by βk(G). In this paper, we have discussed some characterizations of k-metric dimension in terms of some graphical parameters. We have mainly focused on 2-metric dimension of graphs and discussed few characterizations. Further 2-metric dimension of trees is determined and from this result 2- metric dimension of path, cycle and sharp bounds of unicyclic graphs are established

Cite this Research Publication : B. Sooryanarayana and Dr. Geetha K. N., “On the k-Metric Dimension of Graphs”, Journal of Mathematics and Computational Science, vol. 4, no. 5, pp. 861–878, 2014.

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