M. Naeem Azhar

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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)
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)
OBJECTIVES To evaluate the functional outcome, morbidity, and viability of foot salvage in diabetic patients. MATERIALS AND METHODS This prospective case series was conducted from March 2007 to December 2012 at the department of surgery Pakistan Ordnance Factories Hospital, Wah Cantt, Pakistan. 123 males and 26 female patients were included in the study.(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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