According to me, the answer should be option “E- Cannot be determined from the above data.” Reason being-
Blue- always tell truth
white- always tell lie
pink- lie/ truth/ lie/ truth/…..
Now suppose if blue is “A” then on left is white, right is pink and itself is blue. But why cannot blue be option B or option C ? because if we assume blue as option B. then on its left is pink and on its right is also pink and blue always tell truth, so this is not possible
Also if we assume blue as option C then on its left is white and on its right is blue and itself as blue is also not possible. Hence only possiblity of vertex A is blue.
now if B is assumed as pink then on its left is pink which is lie, on its right is again pink which should be true as per question but this is not possible so vertex B has to be white
So as vertex B is white then vertex C is pink
so for whits as option B, its left is pink but this is truth whereas white always tells lie so contradictory.
Hence the solution cannot be determined.