A Note On The Partition Dimension of Thorn of Fan Graph

Abstract

Let be a connected graph and. For a vertex and an ordered k-partition of, the presentation of concerning is the k-vector, where denotes the distance between and for. The k-partition is said to be resolving if for every two vertices, the representation. The minimum k for which there is a resolving k-partition of is called the partition dimension of, denoted by. Let be a non-negative integer, for. The thorn of, with parameters is obtained by attaching vertices of degree one to the vertex, denoted by. In this paper, we determine the partition dimension of where, the fan on n+1 vertices, for.