fishing Prince love tree especially love tree centroid the tree connect graph cyclesA vertex centroid tree cut vertex remove remove edge vertex size large connect component remain graph small possiblefor example centroid follow tree 2 cut size large connect component remain graph 2 can not small however tree centroid example both vertex 1 vertex 2 centroid size large connect component 3 cutting themnow fishing Prince tree he cut edge tree mean remove edge after add edge the result graph operation tree he add edge cuthe want centroid result tree unique help find possible way operation it prove way exist