It has been shown that Y3 [G1 (S)] may be disconnected, even if G1 (S) is connected. Test this theoretical result empirically. Our new conjecture is that, if G1 (S) is connected, then Y3 [G 2 (S)] is always connected. Test this conjecture empirically. We will also discuss the theoretical insight for this conjecture. Could you empirically determine a real value d < 2 for which, Y3 [G 2 (S)] is always connected, if G1 (S) is connected?