In this paper, we consider the effect of subdivision of an edge on the neighbourhood number of a graph. We introduce the concept of neighbourhood subdivision number of a graph as the minimum number of edges that must be subdivided (where each edge in G can be subdivided at most once) in order to increase the neighbourhood number. We show that the neighbourhood subdivision number for a tree is always either one or two. We also provide a constructive characterization of trees whose neighbourhood subdivision number is exactly one and two.

tree, neighbourhood number, neighbourhood subdivision number.