An undirected graph G(V,E) with n vertices and m edges is called to be connected if every pair of the vertices in G exists a path connecting them, otherwise, G is disconnected. A graph can be labeled if only the vertices are labelled and it is called vertex labelling, if only edges are labelled then it is called as edge labelling, and if both vertices and edges are labelled, it is called as total labelling. The edge that has the same starting and end point is called a loop, and two or more edges that connect the same vertices are called parallel edges. A graph is called simple if there is neither loop nor parallel edge on that graph. Given n vertices and m edges there are a lot of possible graphs can be constructed either connected or not, simple or not. In this research we discuss about counting the number of disconnected vertex labelled graph for graph with order maximal four and m ≥ 1. Keywords : counting graph, vertex labelled graph, disconnected, graph order