👉 In mathematics, a Gilbert's theorem is a result in graph theory that states that if G is a simple connected graph with n vertices and m edges, then G has at least 2m-1 edges. This result was first proven by J. E. Gilbert in 1958. The theorem can be stated as follows: If G is a simple connected graph with n vertices and m edges, then G has at least 2m-1 edges. This means that the number