Abstract
All graphs in this paper are undirected and connected graphs. An ordered k-partition set [Formula: see text] where [Formula: see text], the representation of a vertex [Formula: see text] of [Formula: see text] with respect to [Formula: see text] is [Formula: see text] where [Formula: see text] is the distance between the vertex v and the set [Formula: see text] with [Formula: see text] for [Formula: see text]. The partition set [Formula: see text] is a local resolving partition of [Formula: see text] if [Formula: see text] for [Formula: see text] adjacent to [Formula: see text] of [Formula: see text]. The minimum local resolving partition [Formula: see text] is a local partition dimension of [Formula: see text], denoted by [Formula: see text]. In our paper, we found the sharp bounds of the local partition dimension of [Formula: see text] and determine the exact value of some special graph.
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