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A subset W of vertices of a graph G is called a resolving set for G if for every pair of distinct vertices u and v of G, there exists a vertex w∈W such that the distance between u and w is different from the distance between v and w. A resolving set containing a minimum number of vertices is called a metric basis for G and the number of vertices in a metric… (More)

- Imran Javaid, Nayab Khalid Raja, Muhammad Salman, Muhammad Naeem Azhar
- 2013

A k-partition Π = {S 1 , S 1 ,…, S k } of V(G) is resolving if for every pair of distinct vertices u,v in G, there is a set S i in Π so that the minimum distance between u and a vertex of S i is different from the minimum distance between v and a vertex of S i. The minimum k for which there is a resolving k-partition of V(G) is the partition dimension of G… (More)

A family of connected graphs G is said to be a family with constant metric dimension if its metric dimension is finite and does not depend upon the choice of G in G. In this paper, we study the metric dimension of the generalized Petersen graphs P (n, m) for n = 2m + 1 and m ≥ 1 and give partial answer of the question raised in [9]: Is P (n, m) for n ≥ 7… (More)

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