Counting the number of vertexes labeled connected graphs of order five with minimum five edges and maximum ten parallel edges

If given a graph G(V,E) with n vertices and m edges many graphs can be constructed. The graphs constructed maybe connected graphs (there exists at least one path connecting every pair of vertices in the graph) or disconnected; either simple a (contains loop or parallel edges) or not simple. In, this paper we will discuss the formula for counting the number of connected vertex labelled graph of order five (n=5) without loops, witof h minimum five edges and maa y contaiof n maximum ten parallel edges.