To see that the degree of each corner vertex is strictly smaller than the degree of
each non-corner vertex, we compute the degree of a vertex in terms of the number of
“topmost disks” of each vertex. For a given vertex, the topmost disk on each peg i is
defined to be the smallest disk among those stacked on peg i . Therefore, the degree of
a vertex is the sum of the number of legal moves each of its topmost disks can make.
Since a corner vertex has only one topmost disk