Show that there is no (n, d, ρ)-edge expander for ρ > 0.5
Is this statement even true?
My attempt: Let n = 2, then we can have 2 vertices, A and B. Let d = 1, therefore there is an edge between A and B. As the definition of edge expander says that for every subset of size at most n/2 = 1, the number of edges between S and S complement is atleast ρd|S| = 1, hence, ρ = 1 and edge expander exists. Does there exist a proof for the statement or is my counter example good enough?