Bounded-diameter conjecture for finite Goldbach graphs

Let a finite Goldbach graph be a finite graph associated with Goldbach representations, and let a finite near Goldbach graph be a finite graph obtained from the corresponding near Goldbach construction. Bounded-diameter conjecture for finite Goldbach graphs. The diameters of finite Goldbach graphs and finite near Goldbach graphs are bounded by a constant. The paper reports computational evidence that both types of graph are connected with diameter at most $5$ up to $10000$ vertices, but no general bound is established.