The partition dimension of subdivision graph on the star
Amrullah Amrullah, Syahrul Azmi, Harry Soeprianto, Muhammad Turmuzi, Yunita Septriana Anwar · Journal of Physics Conference Series · 2019
Abstract The partition dimension of the graphs is one of the open problems in graph theory. One of the methods which are used researcher is a graph operation, for example, subdivision operations. Let G be a connected graph of order n. The subdivision operation of G is an operation in G that replaces any edge by a path P k i+2 for ki ≥ 1 and i ∈ [1, n]. The result graph of this operation is called the subdivision graph, is denoted by S(G(E; k 1, k 2, ⋯, k n )). Furthermore, if each k i = 1, then the subdivision graph is denoted by S(G). One of the most recent results on the partition dimension of subdivision operation in the general graphs is published by Amrullah, et al 2016. However, the results show only an upper and lower bounds of the subdivision graph partition dimension. Therefore, this paper is devoted to finding the partition dimension of subdivision graph S(G) and S(G(E; k 1, k 2, ⋯, k n )) on special star graphs G = K 1,n .