  The ground state property of the alternating spin ladder is studied in the
case that the system involves an antiferromagnetic intra-chain interaction as
well as two kinds of inter-chain interactions; one is between spins of the same
magnitude and the other is between spins with different magnitudes. The
calculation has been carried out by the exact diagonalization method. As a
consequence of the competition among interactions, the system is revealed to
show an interesting variety of phases in the ground state property. Its phase
diagram is exhibited in the parameter space of the system. We find that,
however small the total amount of the inter-chain interactions is, the
ferrimagnetic ground state becomes unstable in a certain region. In this case,
which of the ferrimagnetic and the singlet ground state to appear is determined
only by the ratio between the inter-chain interactions regardless of their
total amount. The nature of two phases appearing in the singlet region of the
phase diagram and the type of the phase transition between them are also
discussed. The results are ensured by comparing with those of obtained in other
models which are contained in our model as special limiting cases.
