  We obtain the formulae for the numbers of 4-matchings and 5-matchings in
terms of the number of hexagonal faces in (4, 6)-fullerene graphs by studying
structural classification of 6-cycles and some local structural properties,
which correct the corresponding wrong results published. Furthermore, we obtain
a formula for the number of 6-matchings in tubular (4, 6)-fullerenes in terms
of the number of hexagonal faces, and a formula for the number of 6-matchings
in the other (4,6)-fullerenes in terms of the numbers of hexagonal faces and
dual-squares.
