Distinctive power of the alliance polynomial has been studied in previous
works, for instance, it has been proved that the empty, path, cycle, complete,
complete without one edge and star graphs are characterized by its alliance
polynomial. Moreover, it has been proved that the family of alliance polynomial
of regular graphs with small degree is a very special one, since it does not
contain alliance polynomial of graphs other than regular graph with the same
degree. In this work we prove that the alliance polynomial also determines the
wheel graphs.
