  An upper bound of the superbridge index of the connected sum of two knots is
given in terms of the braid index of the summands. Using this upper bound and
minimal polygonal presentations, we give an upper bound in terms of the
superbridge index and the bridge index of the summands when they are torus
knots. In contrast to the fact that the difference between the sum of bridge
indices of two knots and the bridge index of their connected sum is always one,
the corresponding difference for the superbridge index can be arbitrarily
large.
